Nature of Light

Light is a form of electromagnetic radiation. It travels as an electromagnetic wave and transfers energy from one place to another.

Unlike mechanical waves such as sound, water waves, and seismic waves, light does not require particles of matter to carry its energy. Light can travel through empty space.

This is why light from the Sun and distant stars can cross the near-vacuum of space and reach Earth.

Visible light is only a small part of a much larger family of electromagnetic waves called the electromagnetic spectrum.

 

 

 

5

Light as an Electromagnetic Wave

An electromagnetic wave consists of changing:

• electric fields
• magnetic fields

These fields oscillate as the wave travels.

The electric field and magnetic field are perpendicular to each other, and both are perpendicular to the direction in which the wave travels.

Because the oscillations are perpendicular to the direction of travel, electromagnetic waves are classified as transverse waves.

Therefore:

light is an electromagnetic transverse wave.

Electric and Magnetic Fields

The word electromagnetic combines:

electric + magnetic

In an electromagnetic wave:

• the electric field changes
• the magnetic field changes
• the changing fields propagate through space

A simplified representation has:

electric field ⟂ magnetic field

and:

both fields ⟂ direction of wave travel

The symbol ⟂ means perpendicular to.

This is different from a mechanical transverse wave, where particles of matter physically oscillate.

Light Does Not Require a Medium

One of the most important properties of light is that it can travel through a vacuum.

A vacuum is a region containing extremely little matter.

Light does not need:

• air
• water
• glass
• particles
• another material medium

to continue travelling.

This is fundamentally different from mechanical waves.

 

 

 

5

Light from the Sun

The Sun is approximately 150 million kilometres from Earth.

Most of the space between the Sun and Earth contains extremely little matter.

If light required a material medium, sunlight could not travel across this space.

But electromagnetic waves can travel through a vacuum.

Therefore, energy from the Sun can reach Earth as electromagnetic radiation.

This energy is essential for:

• vision
• photosynthesis
• Earth's climate system
• solar energy technologies

Mechanical Waves

A mechanical wave requires a material medium through which to travel.

Examples include:

• sound waves
• water waves
• waves on strings
• seismic waves

The medium can be:

• solid
• liquid
• gas

Particles within the medium oscillate and transfer energy to neighbouring particles.

Light vs Mechanical Waves

The major difference is therefore not whether they behave like waves.

Both do.

The key difference is:

mechanical waves require matter; electromagnetic waves do not.

Light and Sound

Light and sound provide a useful comparison.

Sound:

• mechanical wave
• requires a medium
• cannot travel through a vacuum
• sound in air is longitudinal
• much slower than light

Light:

• electromagnetic wave
• does not require a medium
• travels through a vacuum
• transverse
• travels extremely quickly

This explains why light and sound behave differently in many everyday situations.

Lightning and Thunder

During a thunderstorm, lightning and thunder are produced at approximately the same event.

However, you usually:

see the lightning first

and:

hear the thunder later

This happens because light travels enormously faster than sound.

The delay does not mean that the lightning occurred several seconds before the thunder was produced.

Instead, the two signals travel toward you at very different speeds.

The Electromagnetic Spectrum

Visible light is part of the electromagnetic spectrum.

The main regions, from lower frequency and longer wavelength toward higher frequency and shorter wavelength, are:

radio → microwave → infrared → visible → ultraviolet → X-ray → gamma ray

All of these are electromagnetic waves.

They differ mainly in their:

• frequency
• wavelength
• photon energy

 

 

Visible Light

Visible light is the portion of the electromagnetic spectrum that can normally be detected by the human eye.

It occupies only a very small part of the entire electromagnetic spectrum.

Visible wavelengths are approximately:

380–750 nm

The exact boundaries are approximate because human visual sensitivity does not suddenly stop at one precise wavelength.

A nanometre (nm) is:

1 nm = 0.000000001 m = 10⁻⁹ m

Colours of Visible Light

Visible light contains a range of colours.

A common sequence from longer wavelength toward shorter wavelength is:

red → orange → yellow → green → blue → violet

Red light has a longer wavelength than violet light.

Violet light has a higher frequency than red light.

Therefore, across the visible spectrum:

red → longer wavelength, lower frequency

violet → shorter wavelength, higher frequency

 

 

 

White Light

What we perceive as white light can contain many wavelengths of visible light.

A prism can separate white light into a spectrum of colours.

This happens because different wavelengths of visible light are refracted by slightly different amounts when passing through the prism.

The spreading of light into its component wavelengths is called:

dispersion

Rainbows

Rainbows provide a natural example of visible-light dispersion.

Sunlight enters water droplets in the atmosphere.

The light undergoes processes including:

• refraction
• internal reflection
• dispersion

Different visible wavelengths emerge at different angles.

This produces the familiar range of colours.

 

 

 

5

Wavelength of Light

Like other waves, light has a wavelength.

Symbol:

λ

Wavelength is the distance between corresponding points of successive wave cycles.

For visible light, wavelength is extremely small and is commonly measured in:

nanometres (nm)

For example, visible green light might have a wavelength near:

550 nm

Convert to metres:

550 nm = 550 × 10⁻⁹ m

= 5.50 × 10⁻⁷ m

Frequency of Light

Light also has a frequency.

Symbol:

f

Frequency is the number of complete oscillations occurring each second.

Unit:

hertz (Hz)

Visible-light frequencies are extremely high, on the order of hundreds of trillions of hertz.

Frequency and wavelength are inversely related when wave speed is fixed.

Therefore:

higher frequency → shorter wavelength

lower frequency → longer wavelength

The Speed of Light

The speed of light in a vacuum is one of the fundamental constants of physics.

Its exact defined value is:

c = 299 792 458 m/s

For most school calculations, this is rounded to:

c ≈ 3.00 × 10⁸ m/s

This means light travels approximately:

300 000 000 metres every second

or:

300 000 kilometres every second

The symbol c is normally used for the speed of light in a vacuum.

How Fast Is Light?

At approximately 300 000 km/s, light could theoretically travel a distance equal to about 7.5 times Earth's circumference in one second.

Even at this enormous speed, light still takes time to travel across astronomical distances.

For example, sunlight takes approximately:

8 minutes 20 seconds

to reach Earth.

When we observe the Sun, we therefore see it as it was several minutes earlier.

Light from the Moon

The Moon is roughly:

384 000 km

from Earth on average.

Light takes approximately:

time = distance/speed

time ≈ 384 000/300 000

time ≈ 1.28 s

to travel from the Moon to Earth.

This means the Moon we see is being observed as it was about 1.3 seconds earlier.

Light from Stars

Stars are much farther away.

Astronomers often describe these distances using light-years.

A light-year is a unit of distance, not time.

It is the distance light travels through a vacuum in one year.

One light-year is approximately:

9.46 × 10¹² km

When we observe a star 100 light-years away, we see light that began its journey approximately 100 years ago.

Astronomy therefore allows us to look into the past.

The Wave Equation for Light

The general wave relationship is:

v = fλ

For electromagnetic waves travelling in a vacuum:

c = fλ

where:

c = speed of light in vacuum

f = frequency

λ = wavelength

Because c is constant in a vacuum, frequency and wavelength must change inversely.

If frequency increases:

wavelength decreases

If wavelength increases:

frequency decreases

Worked Example: Finding Frequency

Suppose visible light has a wavelength of:

600 nm

First convert to metres:

600 nm = 600 × 10⁻⁹ m

λ = 6.00 × 10⁻⁷ m

Use:

c = fλ

Rearrange:

f = c/λ

Substitute:

f = (3.00 × 10⁸)/(6.00 × 10⁻⁷)

f = 5.00 × 10¹⁴ Hz

Worked Example: Finding Wavelength

An electromagnetic wave has a frequency of:

6.00 × 10¹⁴ Hz

Use:

c = fλ

Rearrange:

λ = c/f

Substitute:

λ = (3.00 × 10⁸)/(6.00 × 10¹⁴)

λ = 5.00 × 10⁻⁷ m

Convert to nanometres:

λ = 500 nm

This wavelength lies within the visible region.

Light Slows Down in Materials

The value:

3.00 × 10⁸ m/s

is the speed of light in a vacuum.

Light generally travels more slowly through materials such as:

• air
• water
• glass
• plastics

For example, light travels more slowly through glass than through a vacuum.

This change in speed is important in explaining refraction.

Light Entering a New Medium

When light crosses from one transparent medium into another:

• its speed can change
• its wavelength can change
• its direction can change
• its frequency remains the same across the boundary

For example, when light enters glass from air, it slows down.

Since:

v = fλ

and frequency remains constant, a decrease in speed means:

wavelength decreases

Refraction

Refraction is the change in direction of a wave associated with a change in wave speed as it enters a different medium.

Light commonly refracts when travelling between:

• air and water
• air and glass
• glass and air

This is why objects underwater can appear displaced from their actual positions.

It is also fundamental to the operation of lenses.

 

 

 

5

Reflection

Light can also undergo reflection.

Reflection occurs when light encounters a surface and some of the wave energy returns.

Examples include:

• mirrors
• reflections from water
• shiny metal surfaces
• reflected sunlight from the Moon

We see most ordinary objects because light reflects from them and enters our eyes.

Diffraction

Light can undergo diffraction, meaning that it can spread when passing through an opening or around an obstacle.

Diffraction is particularly noticeable when the size of the opening or obstacle is comparable to the wavelength.

Because visible-light wavelengths are extremely small, noticeable diffraction usually requires very small openings or structures.

Diffraction provides important evidence for the wave nature of light.

Interference

When light waves overlap, they can undergo interference.

The waves combine according to the principle of superposition.

They can produce:

• constructive interference
• destructive interference

Interference patterns provide further evidence that light behaves as a wave.

Polarization

Because light is a transverse electromagnetic wave, it can be polarized.

Polarization restricts the orientation of the electromagnetic oscillations.

Applications include:

• polarized sunglasses
• photography
• LCD displays
• scientific instruments

The ability of light to be polarized is strong evidence for its transverse nature.

Electromagnetic Waves Beyond Visible Light

Visible light represents only the portion our eyes detect.

The rest of the electromagnetic spectrum is invisible to human vision.

Radio waves

Used in communication and broadcasting.

Microwaves

Used in communication, radar, and microwave heating.

Infrared

Associated with thermal radiation and used in thermal imaging.

Visible light

Detected by human eyes.

Ultraviolet

Produced strongly by the Sun and used in several technologies.

X-rays

Used in imaging and scientific analysis.

Gamma rays

Very high-frequency electromagnetic radiation associated with nuclear and high-energy processes.

All are electromagnetic waves.

Comparing Regions of the Electromagnetic Spectrum

Moving from radio toward gamma:

wavelength decreases

while:

frequency increases

Visible Light's Position

Visible light lies between:

infrared

and:

ultraviolet

in the electromagnetic spectrum.

Therefore, the order around visible light is:

infrared → visible → ultraviolet

Infrared has:

• longer wavelength
• lower frequency

than visible light.

Ultraviolet has:

• shorter wavelength
• higher frequency

than visible light.

Light Carries Energy

Electromagnetic waves transfer energy.

Examples include:

• sunlight warming Earth's surface
• solar cells receiving energy from sunlight
• infrared radiation heating objects
• light producing chemical changes in photosynthesis
• electromagnetic radiation carrying information in communication systems

Light can therefore transfer energy even across empty space.

Light Carries Information

Light is also one of our most important sources of information.

When light reaches our eyes, it can tell us about:

• colour
• shape
• position
• movement
• brightness
• texture

Scientific instruments can analyze light to determine properties of distant objects.

Astronomers, for example, study electromagnetic radiation to investigate stars and galaxies that cannot be visited directly.

Light and Communication

Electromagnetic waves can carry information over large distances.

Visible and near-infrared light can be used in fibre-optic communication.

Information can be encoded into rapidly changing light signals and transmitted through optical fibres.

This allows large amounts of information to be transferred very quickly.

Light as More Than a Simple Classical Wave

Describing light as an electromagnetic wave explains phenomena such as:

• reflection
• refraction
• diffraction
• interference
• polarization

However, modern physics shows that light also has particle-like properties.

Light energy can be transferred in packets called:

photons

This is known as wave-particle duality.

For understanding the basic nature and propagation of light, the electromagnetic-wave model is extremely important.

Comparing Sound and Light in Space

Imagine an explosion occurring in space.

Visible light from the event could travel through the vacuum and potentially reach a distant observer.

Ordinary sound could not travel through the empty space because sound requires a material medium.

Therefore:

light can cross a vacuum

sound cannot cross a vacuum

This comparison clearly demonstrates the difference between electromagnetic and mechanical waves.

A Complete Example

A beam of visible light has:

λ = 450 nm

Convert to metres:

450 nm = 4.50 × 10⁻⁷ m

Use:

c = fλ

Rearrange:

f = c/λ

f = (3.00 × 10⁸)/(4.50 × 10⁻⁷)

f ≈ 6.67 × 10¹⁴ Hz

A wavelength of 450 nm lies in the visible region, toward the blue part of the spectrum.

The wave can travel through a vacuum because it is electromagnetic rather than mechanical.

A Reliable Strategy for Analyzing Light

When examining a problem involving light:

1. Identify whether the wave is electromagnetic or mechanical.
2. Determine whether a material medium is required.
3. Identify the wavelength or frequency if provided.
4. Determine where the radiation lies within the electromagnetic spectrum.
5. Use c = 3.00 × 10⁸ m/s for light travelling in a vacuum.
6. Use c = fλ when frequency or wavelength must be calculated in vacuum.
7. Convert units carefully, especially nm to m.
8. Remember that frequency and wavelength are inversely related for a fixed wave speed.
9. If light enters another material, remember that its speed and wavelength can change while its frequency remains constant.
10. Identify wave behaviours such as reflection, refraction, diffraction, interference, or polarization when relevant.

Common Mistakes

Thinking light requires air

Light can travel through a vacuum.

Thinking electromagnetic waves contain vibrating air particles

Electromagnetic waves consist of oscillating electric and magnetic fields.

Thinking visible light is the entire electromagnetic spectrum

Visible light is only a small region of the spectrum.

Thinking sound and light are the same type of wave

Sound is mechanical. Light is electromagnetic.

Thinking all electromagnetic waves are visible

Human eyes detect only the visible region.

Thinking red light has a higher frequency than violet light

Red has a longer wavelength and lower frequency than violet.

Thinking light always travels at exactly 3.00 × 10⁸ m/s

That value applies to a vacuum. Light travels more slowly through materials.

Thinking frequency changes when light enters glass

Frequency remains constant across the boundary; speed and wavelength change.

Thinking a light-year is a unit of time

A light-year is a unit of distance.

Forgetting to convert nanometres into metres

Remember:

1 nm = 10⁻⁹ m

before using SI units in calculations.

Key Terms

Light — electromagnetic radiation, with visible light being the portion detectable by human vision.

Electromagnetic wave — wave consisting of oscillating electric and magnetic fields.

Electromagnetic radiation — energy transmitted through space as electromagnetic waves.

Electric field — region in which an electric charge experiences an electric force.

Magnetic field — region in which magnetic effects can be detected.

Transverse wave — wave whose oscillations are perpendicular to the direction of travel.

Mechanical wave — wave that requires a material medium.

Medium — matter through which a mechanical wave travels.

Vacuum — region containing extremely little matter.

Electromagnetic spectrum — complete range of electromagnetic radiation arranged by wavelength or frequency.

Visible light — electromagnetic radiation detectable by the human eye.

Wavelength (λ) — distance between corresponding points on consecutive wave cycles.

Frequency (f) — number of complete oscillations per second.

Hertz (Hz) — SI unit of frequency.

Nanometre (nm) — one billionth of a metre, or 10⁻⁹ m.

Speed of light (c) — speed of electromagnetic radiation in a vacuum, approximately 3.00 × 10⁸ m/s.

Reflection — return of wave energy from a boundary.

Refraction — change in wave direction associated with a change in wave speed.

Diffraction — spreading of waves around obstacles or through openings.

Interference — combination of overlapping waves.

Polarization — restriction of transverse oscillations to particular orientations.

Dispersion — separation of light according to wavelength.

Photon — quantum, or packet, of electromagnetic energy.

Light-year — distance travelled by light through a vacuum in one year.

Key Takeaways

• Light is electromagnetic radiation.
• Light behaves as a transverse electromagnetic wave.
• Electromagnetic waves consist of oscillating electric and magnetic fields.
• The electric and magnetic fields are perpendicular to each other and to the direction of wave travel.
• Light does not require a material medium.
• Light can travel through a vacuum.
• Mechanical waves require matter through which to travel.
• Sound is mechanical, while light is electromagnetic.
• Visible light is only a small part of the electromagnetic spectrum.
• The electromagnetic spectrum includes radio, microwave, infrared, visible, ultraviolet, X-ray, and gamma radiation.
• Visible light lies between infrared and ultraviolet.
• Red visible light has a longer wavelength and lower frequency than violet light.
• Violet light has a shorter wavelength and higher frequency than red light.
• Light travels through a vacuum at approximately 3.00 × 10⁸ m/s.
• The wave relationship for light in a vacuum is c = fλ.
• At constant speed, wavelength and frequency are inversely related.
• Light travels more slowly through materials than through a vacuum.
• When light enters another medium, its frequency remains constant while its speed and wavelength may change.
• Light can undergo reflection, refraction, diffraction, interference, and polarization.
• Light transfers energy and information.
• The ability of sunlight to cross space demonstrates that electromagnetic waves do not require a medium.
• Light from distant astronomical objects takes time to reach us.
• A light-year is a unit of distance.
• The electromagnetic-wave model explains many important properties of light, although modern physics also reveals particle-like behaviour through photons.

Check Your Understanding

1. Describe light as an electromagnetic wave.
2. What oscillates in an electromagnetic wave?
3. Explain why light is classified as a transverse wave.
4. Compare light and mechanical waves in terms of their need for a medium.
5. Explain why sunlight can travel from the Sun to Earth while ordinary sound cannot travel through the same region of space.
6. List the seven major regions of the electromagnetic spectrum in order from longest wavelength to shortest wavelength.
7. Where is visible light located within the electromagnetic spectrum?
8. Compare red and violet visible light in terms of wavelength and frequency.
9. State the approximate speed of light in a vacuum in both m/s and km/s.
10. A beam of light has a wavelength of 500 nm. Convert this wavelength into metres.
11. Calculate the frequency of light with a wavelength of 500 nm using c = 3.00 × 10⁸ m/s.
12. Explain why we normally see lightning before hearing thunder.
13. Describe what happens to the speed, frequency, and wavelength of light when it travels from a vacuum into a transparent material where it moves more slowly.
14. A student says, "Light must need air because we can see light travelling through the atmosphere." Explain why this reasoning is incorrect.
15. Explain how observations of sunlight, starlight, reflection, refraction, diffraction, interference, and polarization provide evidence for the electromagnetic wave nature of light.

Reflection and Mirrors

Reflection occurs when light strikes a surface and changes direction so that it travels back into the original medium.

Mirrors produce clear reflections because their smooth surfaces reflect light in predictable directions. By applying the law of reflection and drawing ray diagrams, we can predict where an image will appear and describe its characteristics.

The three main mirror types are:

• plane mirrors — flat reflecting surfaces
• concave mirrors — curved inward
• convex mirrors — curved outward

Each type produces images with different characteristics and has different practical applications.

 

 

 

7

Reflection of Light

When light reaches a boundary, several things can happen.

Light may be:

• reflected
• transmitted
• absorbed
• refracted

With a mirror, a large proportion of the visible light is reflected.

The incoming light ray is called the incident ray.

The ray leaving the surface is called the reflected ray.

The Normal

To describe reflection accurately, we draw an imaginary line called the normal.

The normal:

• passes through the point where the light strikes the surface
• is perpendicular to the reflecting surface

Therefore, the normal makes a:

90° angle with the mirror surface

Angles of reflection are measured relative to the normal, not relative to the mirror.

Angle of Incidence

The angle of incidence, often written as θᵢ, is the angle between:

incident ray and normal

It is not the angle between the incident ray and the mirror surface.

For example, if an incident ray makes an angle of 35° with the normal:

θᵢ = 35°

Angle of Reflection

The angle of reflection, often written as θᵣ, is the angle between:

reflected ray and normal

According to the law of reflection:

angle of incidence = angle of reflection

or:

θᵢ = θᵣ

 

The Law of Reflection

The law of reflection states:

The angle of incidence equals the angle of reflection.

Therefore:

θᵢ = θᵣ

If:

θᵢ = 20°

then:

θᵣ = 20°

If:

θᵢ = 55°

then:

θᵣ = 55°

The angles must always be measured from the normal.

Worked Example: Reflection

A ray strikes a plane mirror at an angle of 42° to the normal.

Determine the angle of reflection.

Using:

θᵢ = θᵣ

θᵢ = 42°

Therefore:

θᵣ = 42°

Measuring from the Mirror Surface

Sometimes an angle is given relative to the mirror rather than the normal.

Remember:

normal ⟂ mirror

Therefore:

angle to normal + angle to mirror = 90°

Suppose a ray makes an angle of 30° with the mirror.

Then:

θᵢ = 90° − 30°

θᵢ = 60°

Therefore:

θᵣ = 60°

This is a common source of mistakes.

Regular Reflection

A smooth surface produces regular reflection, sometimes called specular reflection.

Parallel incoming rays remain organized after reflection.

Examples include:

• mirrors
• calm water
• polished metal
• smooth glass surfaces

Because the reflected rays remain organized, a clear image can be formed.

Diffuse Reflection

A rough surface produces diffuse reflection.

Different parts of the surface have normals pointing in slightly different directions.

As a result, incoming parallel rays are reflected in many directions.

Examples include:

• paper
• walls
• clothing
• rough wood
• unpolished stone

The law of reflection still applies at every point.

The surface is simply oriented differently at different microscopic locations.

 

Why We Can See Ordinary Objects

Most objects around us do not produce their own visible light.

Instead, light from a source such as:

• the Sun
• a lamp
• a screen

strikes the object.

Some of this light reflects toward our eyes.

Diffuse reflection allows objects to be seen from many different directions.

Without reflected light reaching our eyes, we cannot see an object.

Plane Mirrors

A plane mirror has a flat reflecting surface.

Examples include:

• bathroom mirrors
• dressing mirrors
• decorative mirrors
• some optical instruments

Plane mirrors produce predictable images.

The image formed by a plane mirror is:

• virtual
• upright
• same size as the object
• same distance behind the mirror as the object is in front
• laterally inverted

Real and Virtual Images

A real image forms where light rays actually converge.

A real image can usually be projected onto a screen.

A virtual image forms where light rays only appear to originate.

The rays do not actually meet at the virtual image position.

A plane mirror produces a:

virtual image

This is why the image appears to be behind the mirror even though the reflected light remains in front of it.

Image Distance in a Plane Mirror

For a plane mirror:

image distance = object distance

If a student stands:

2 m in front of a mirror

the image appears:

2 m behind the mirror

Therefore, the distance between the student and the image is:

2 + 2

= 4 m

Worked Example: Plane Mirror Distance

A person stands 1.5 m from a plane mirror.

The image appears:

1.5 m behind the mirror

The distance between the person and the image is:

1.5 + 1.5

= 3.0 m

If the person moves 0.5 m toward the mirror, the new object distance is:

1.0 m

The new image distance is also:

1.0 m

The person and image are now:

2.0 m apart

Constructing a Plane-Mirror Ray Diagram

A ray diagram uses light rays to determine where an image appears.

To construct an image in a plane mirror:

1. Draw the mirror as a straight line.
2. Draw the object in front of the mirror.
3. Select a point on the object, usually its top.
4. Draw at least two rays from that point toward the mirror.
5. At each point of reflection, draw or imagine the normal.
6. Reflect each ray using θᵢ = θᵣ.
7. Extend the reflected rays backward behind the mirror using dashed lines.
8. Locate the point where the backward extensions meet.
9. Repeat if necessary for another point on the object.
10. Draw the virtual image.

The dashed lines represent where the reflected rays appear to originate.

 

 

 

8

Image Characteristics of a Plane Mirror

A useful way to describe an image is to ask:

What type is it?

Virtual.

Which orientation?

Upright.

What size?

Same size as the object.

Where is it?

Same distance behind the mirror as the object is in front.

This gives a complete description of a plane-mirror image.

Lateral Inversion

A plane-mirror image is laterally inverted.

This is often described as an apparent left-right reversal.

For example, writing viewed in a mirror appears reversed.

However, the mirror is more precisely reversing the front-back direction relative to the mirror rather than physically swapping left and right.

For introductory work, the term lateral inversion is commonly used.

Curved Mirrors

Not all mirrors are flat.

Two important types of curved mirrors are:

• concave mirrors
• convex mirrors

Their curved surfaces cause reflected rays to converge or diverge.

As a result, their image characteristics differ from those of plane mirrors.

Concave Mirrors

A concave mirror curves inward.

A useful memory aid is:

concave → cave

The reflecting surface resembles the inside of a curved bowl.

Parallel rays travelling toward a concave mirror are reflected toward a point called the:

principal focus

Concave mirrors are therefore converging mirrors.

 

 

 

6

Principal Axis

The principal axis is an imaginary straight line passing through the centre of a spherical mirror.

Important points are positioned along this axis.

For a concave mirror, these commonly include:

• pole or vertex
• focal point, F
• centre of curvature, C

Focal Point

The focal point, F, is the point where rays travelling parallel to the principal axis converge after reflection from a concave mirror.

The distance from the mirror to the focal point is called the:

focal length

symbol:

f

Centre of Curvature

For a spherical mirror, the centre of curvature, C, is the centre of the imaginary sphere of which the mirror forms a part.

For an ideal spherical mirror:

C is approximately twice as far from the mirror as F

Therefore:

radius of curvature ≈ 2f

or:

R ≈ 2f

Principal Rays for a Concave Mirror

Several standard rays make ray diagrams easier.

Parallel ray

A ray travelling parallel to the principal axis reflects through F.

Focal ray

A ray travelling through F reflects parallel to the principal axis.

Centre-of-curvature ray

A ray travelling toward C reflects back along approximately the same path.

Using any two suitable principal rays is normally enough to locate an image.

Concave Mirror: Object Beyond C

If an object is placed beyond the centre of curvature:

object → C → F → mirror

the image forms:

• between C and F
• real
• inverted
• smaller than the object

This arrangement can produce a reduced real image.

Concave Mirror: Object at C

If the object is at C, the image forms at C.

The image is:

• real
• inverted
• same size as the object

Concave Mirror: Object Between C and F

If the object is between C and F, the reflected rays converge beyond C.

The image is:

• real
• inverted
• enlarged

This arrangement can produce a magnified real image.

 

 

 

4

Concave Mirror: Object at F

If the object is placed at the focal point, reflected rays leave approximately parallel.

The image is effectively located extremely far away in the idealized model.

This position is important in devices designed to produce approximately parallel beams.

Concave Mirror: Object Inside F

If the object is between the focal point and the mirror, the reflected rays diverge.

Their backward extensions meet behind the mirror.

The image is:

• virtual
• upright
• enlarged
• behind the mirror

This is why concave mirrors can be used as magnifying mirrors.

Concave Mirror Image Summary

The image formed by a concave mirror therefore depends strongly on the object's position.

Convex Mirrors

A convex mirror curves outward toward the object.

Parallel rays striking a convex mirror spread apart after reflection.

Convex mirrors are therefore diverging mirrors.

The reflected rays appear to originate from a focal point behind the mirror.

 

 

 

7

Images in Convex Mirrors

For an ordinary real object placed in front of a convex mirror, the image is always:

• virtual
• upright
• smaller than the object
• behind the mirror

The image position changes as the object moves, but these general characteristics remain the same.

Why Convex Mirrors Give a Wider View

Because reflected rays diverge, a convex mirror can collect light from a wider range of directions.

This produces a wider field of view than a plane mirror of similar size.

The trade-off is that objects appear smaller.

This makes convex mirrors useful when seeing a large area is more important than seeing a large image.

Comparing Mirror Types

Applications of Plane Mirrors

Plane mirrors are used when an undistorted, same-size virtual image is useful.

Applications include:

• bathroom mirrors
• dressing mirrors
• interior decoration
• optical instruments
• periscopes

A simple periscope can use two plane mirrors to redirect light.

Periscopes

A simple periscope uses reflection to allow someone to see over or around an obstacle.

Two mirrors may be placed at suitable angles inside a tube.

Light from the object:

1. strikes the upper mirror
2. reflects downward
3. strikes the lower mirror
4. reflects toward the observer

Each reflection obeys the law:

θᵢ = θᵣ

Applications of Concave Mirrors

Concave mirrors are useful when light needs to be:

• focused
• collected
• magnified
• directed into a beam

Applications include:

• makeup mirrors
• shaving mirrors
• some dental mirrors
• reflecting telescopes
• solar concentrators
• some vehicle headlights
• flashlights

 

 

 

7

Magnifying Mirrors

When a person's face is positioned closer to a concave mirror than its focal length, the mirror forms an image that is:

• virtual
• upright
• enlarged

This makes small details easier to see.

The same principle can be useful in some makeup and shaving mirrors.

Reflecting Telescopes

A reflecting telescope uses a curved mirror to collect light from distant objects.

Light from a very distant astronomical object arrives in nearly parallel rays.

A concave primary mirror reflects these rays toward a focus.

A telescope can therefore collect much more light than the human eye alone.

This allows astronomers to observe faint objects.

Reflectors in Headlights

A light source placed near the focal point of a concave or specially shaped reflector can produce a beam in which the reflected rays are approximately parallel.

This principle is used in devices such as:

• headlights
• flashlights
• searchlights

The arrangement is essentially the reverse of focusing parallel incoming rays.

Applications of Convex Mirrors

Convex mirrors are useful when a wide field of view is required.

Applications include:

• vehicle side mirrors
• security mirrors
• parking garages
• shop surveillance
• road intersections
• blind corners

Because the images are smaller, more of the surroundings can fit into the mirror.

 

 

 

7

Vehicle Mirrors

Convex mirrors are often used where drivers need a wider view.

A convex mirror makes objects appear:

smaller

and therefore they may appear farther away than expected.

This is why some vehicle mirrors carry warnings indicating that objects may be closer than they appear.

The wider field of view helps reduce blind spots.

Security Mirrors

Convex mirrors are commonly installed in:

• shops
• warehouses
• hospitals
• parking garages
• corridors

One mirror can provide a view of a relatively large area.

This makes it easier to see around corners or monitor locations that would otherwise be hidden.

Real Images

A real image forms where reflected light rays actually meet.

Real images can usually be projected onto a screen.

Concave mirrors can produce real images when the object is beyond the focal point.

Real images produced by a concave mirror are generally:

inverted

Virtual Images

A virtual image forms where rays only appear to originate.

The light rays do not actually pass through the virtual image location.

Virtual images cannot normally be projected directly onto a screen.

Examples include images produced by:

• plane mirrors
• convex mirrors
• concave mirrors when the object is inside the focal length

Determining Image Characteristics

When describing a mirror image, consider four questions.

Type

Is it real or virtual?

Orientation

Is it upright or inverted?

Size

Is it larger, smaller, or the same size?

Position

Where is the image relative to the mirror, focal point, and centre of curvature?

These characteristics provide a complete description of the image.

Ray Diagram Example: Plane Mirror

Suppose an arrow is placed 4 cm in front of a plane mirror.

Its image will be:

• 4 cm behind the mirror
• virtual
• upright
• the same height as the object

The object-to-image distance is:

4 + 4

= 8 cm

The ray diagram should show reflected rays in front of the mirror and dashed backward extensions behind it.

Ray Diagram Example: Concave Mirror

Suppose an object is positioned beyond C.

Draw:

1. a ray parallel to the principal axis, which reflects through F
2. a ray directed through C, which reflects back along its path

The reflected rays intersect between:

C and F

Therefore the image is:

• real
• inverted
• smaller

Ray Diagram Example: Convex Mirror

For a convex mirror:

1. draw a ray parallel to the principal axis
2. reflect it so that it appears to originate from F behind the mirror
3. draw another suitable ray
4. extend the reflected rays backward using dashed lines

The backward extensions intersect behind the mirror.

Therefore the image is:

• virtual
• upright
• smaller

Image Characteristics from Ray Diagrams

Ray diagrams are more than drawings.

They allow us to predict physical image characteristics.

If actual reflected rays meet:

real image

If only backward extensions meet:

virtual image

If the image arrow points opposite to the object:

inverted

If it points in the same direction:

upright

Compare image and object heights to determine:

• enlarged
• same size
• reduced

Reflection and Safety

Mirrors can improve safety by increasing visibility.

Convex mirrors are particularly useful because they allow people to see:

• around corners
• approaching vehicles
• hidden aisles
• blind spots

However, the reduced image size can make judging distance more difficult.

Mirror design therefore involves balancing:

field of view against image size and apparent distance.

Mirrors in Solar Energy

Concave reflecting surfaces can concentrate sunlight.

Parallel rays from the Sun can be reflected toward a smaller region.

This can produce high temperatures.

Solar concentrating systems can use this energy for:

• heating
• generating steam
• producing electricity
• industrial processes

This is an example of using the converging properties of curved reflectors.

Mirrors in Scientific Instruments

Mirrors are important components in many scientific systems.

Examples include:

• telescopes
• microscopes
• spectrometers
• lasers
• optical experiments

Mirrors can redirect, focus, or control light without requiring the light to pass through a transparent material.

A Reliable Strategy for Reflection Problems

When solving a reflection problem:

1. Identify the reflecting surface.
2. Locate the point where the incident ray strikes.
3. Draw the normal perpendicular to the surface.
4. Identify the angle of incidence.
5. Make sure the angle is measured from the normal.
6. Apply θᵢ = θᵣ.
7. Draw the reflected ray.
8. If constructing an image, use at least two rays.
9. Extend reflected rays backward with dashed lines if locating a virtual image.
10. Identify the image position.
11. State whether the image is real or virtual.
12. State whether it is upright or inverted.
13. Compare its size with the object.
14. Check that every reflection obeys the law of reflection.

Common Mistakes

Measuring angles from the mirror

Angles of incidence and reflection are measured from the normal.

Drawing the normal parallel to the mirror

The normal must be perpendicular to the reflecting surface.

Thinking the angle of reflection can be different from the angle of incidence

For reflection:

θᵢ = θᵣ

Thinking diffuse reflection breaks the law of reflection

Each ray still obeys the law locally.

Thinking the image in a plane mirror is on the mirror surface

It appears behind the mirror.

Thinking a plane mirror makes an image smaller

A plane-mirror image is the same size as the object.

Thinking light actually travels behind a plane mirror

The backward ray extensions are imaginary construction lines. The reflected rays remain in front of the mirror.

Thinking all concave-mirror images are enlarged

Concave mirrors can produce smaller, same-size, or larger images depending on object position.

Thinking concave mirrors always form real images

An object inside the focal length produces a virtual image.

Thinking convex mirrors form enlarged images

For ordinary real objects, convex mirrors produce reduced virtual images.

Confusing concave and convex mirrors

Concave curves inward and converges parallel rays.

Convex curves outward and diverges parallel rays.

Drawing virtual rays as solid lines behind the mirror

Backward extensions are conventionally shown as dashed lines.

Key Terms

Reflection — change in direction of a wave when it returns from a boundary.

Incident ray — incoming light ray travelling toward a reflecting surface.

Reflected ray — light ray travelling away from a reflecting surface.

Normal — imaginary line perpendicular to a surface at the point of incidence.

Angle of incidence (θᵢ) — angle between the incident ray and the normal.

Angle of reflection (θᵣ) — angle between the reflected ray and the normal.

Law of reflection — rule stating that the angle of incidence equals the angle of reflection.

Regular reflection — organized reflection from a smooth surface.

Diffuse reflection — reflection in many directions from a rough surface.

Plane mirror — mirror with a flat reflecting surface.

Concave mirror — inward-curving mirror that can converge parallel rays.

Convex mirror — outward-curving mirror that causes parallel reflected rays to diverge.

Principal axis — reference line passing through the centre of a spherical mirror.

Focal point (F) — point through which parallel reflected rays converge, or from which they appear to diverge.

Focal length (f) — distance between a mirror and its focal point.

Centre of curvature (C) — centre of the imaginary sphere associated with a spherical mirror.

Real image — image formed where light rays actually converge.

Virtual image — image formed where rays appear to originate but do not actually converge.

Lateral inversion — apparent side-to-side reversal associated with a plane-mirror image.

Field of view — amount of the surroundings visible through an optical system.

Ray diagram — diagram showing the paths taken by light rays.

Converging mirror — mirror that causes parallel rays to move toward a focus; a concave mirror.

Diverging mirror — mirror that causes parallel reflected rays to spread apart; a convex mirror.

Key Takeaways

• Reflection occurs when light returns from a surface.
• The incident ray travels toward the surface.
• The reflected ray travels away from the surface.
• The normal is perpendicular to the reflecting surface.
• Angles of incidence and reflection are measured from the normal.
• The law of reflection states θᵢ = θᵣ.
• Smooth surfaces produce regular reflection.
• Rough surfaces produce diffuse reflection, but each ray still obeys the law of reflection.
• Plane mirrors produce virtual, upright, same-size images.
• A plane-mirror image appears the same distance behind the mirror as the object is in front.
• Plane-mirror images are laterally inverted.
• Concave mirrors curve inward and converge parallel rays.
• Concave mirrors can produce real or virtual images.
• The characteristics of a concave-mirror image depend on the object's position relative to F and C.
• Convex mirrors curve outward and cause reflected rays to diverge.
• Convex mirrors produce virtual, upright, reduced images for ordinary real objects.
• Convex mirrors provide a wide field of view.
• Real images form where actual light rays converge.
• Virtual images form where rays only appear to originate.
• Ray diagrams can determine image position, orientation, size, and type.
• Plane mirrors are useful for ordinary viewing and optical systems.
• Concave mirrors are useful for focusing light and magnification.
• Convex mirrors are useful when a wide field of view is required.
• Mirror applications include telescopes, headlights, security systems, vehicle mirrors, periscopes, and solar-energy systems.
• Understanding the law of reflection allows mirror behaviour to be predicted rather than simply memorized.

Check Your Understanding

1. State the law of reflection.
2. Define the incident ray, reflected ray, and normal.
3. A ray strikes a mirror at 28° to the normal. Determine the angle of reflection.
4. A ray makes an angle of 25° with the mirror surface. Determine its angle of incidence and angle of reflection.
5. Explain why a rough wall can still obey the law of reflection even though it does not produce a clear image.
6. Describe the four main characteristics of an image produced by a plane mirror.
7. A student stands 2.5 m in front of a plane mirror. How far behind the mirror does the image appear, and what is the distance between the student and the image?
8. Describe how to construct a ray diagram for an object viewed in a plane mirror.
9. Explain the difference between a real image and a virtual image.
10. An object is placed beyond C in front of a concave mirror. Describe the image's position, type, orientation, and relative size.
11. An object is moved between F and a concave mirror. Describe how the resulting image differs from the image formed when the object is beyond F.
12. Describe the image normally produced by a convex mirror and explain why convex mirrors are useful for vehicle and security applications.
13. Compare plane, concave, and convex mirrors in terms of shape, effect on reflected rays, and typical image characteristics.
14. Explain why placing a light source near the focal point of a concave reflector can produce an approximately parallel beam in a flashlight or headlight.
15. A school wants mirrors for three locations: a bathroom, a blind corridor corner, and a small reflecting telescope. Choose the most appropriate mirror type for each location and justify each choice using the image or reflection properties of the mirror.

Refraction and Lenses

Refraction is the change in direction of light when it passes from one transparent medium into another and its speed changes.

For example, light may travel from:

• air into water
• air into glass
• glass into air
• water into air

Because light travels at different speeds in different materials, its direction may change at the boundary between them.

This behaviour allows lenses to focus or spread light and is the basis of technologies such as:

• glasses
• contact lenses
• cameras
• microscopes
• telescopes
• magnifying glasses
• projectors

 

 

 

7

Why Light Refracts

Light travels fastest in a vacuum.

In transparent materials such as glass or water, light travels more slowly because of its interaction with the material.

When light crosses a boundary and its speed changes, its direction can also change.

This change in direction is called:

refraction

The amount of bending depends on:

• the materials involved
• the angle at which the light reaches the boundary
• the wavelength of the light

The Normal

As with reflection, refraction angles are measured from an imaginary line called the normal.

The normal is:

perpendicular to the boundary

at the point where the light ray crosses it.

Angles are measured between:

ray and normal

not between the ray and the surface.

Angle of Incidence

The angle of incidence, θᵢ, is the angle between:

incident ray and normal

The incident ray is the incoming ray approaching the boundary.

Angle of Refraction

The angle of refraction, θᵣ, is the angle between:

refracted ray and normal

The refracted ray is the ray travelling through the second medium.

Unlike reflection:

θᵢ and θᵣ are not generally equal.

 

 

 

5

Bending Toward the Normal

When light enters a medium in which it travels more slowly, the ray normally bends:

toward the normal

For example:

air → glass

Light slows down.

Therefore, for an angled ray:

angle of refraction < angle of incidence

The refracted ray is closer to the normal.

Bending Away from the Normal

When light enters a medium in which it travels faster, the ray normally bends:

away from the normal

For example:

glass → air

Light speeds up.

Therefore:

angle of refraction > angle of incidence

for angles below the critical angle.

A Useful Refraction Rule

A useful summary is:

faster → slower: toward the normal

slower → faster: away from the normal

This rule works when light strikes the boundary at an angle.

Light Travelling Along the Normal

Suppose light strikes a boundary directly along the normal.

Then:

θᵢ = 0°

The light changes speed when it enters the new medium, but it does not change direction.

Therefore:

a change in speed does not always produce visible bending.

The direction changes only when the light enters the new medium at an angle to the normal.

What Changes During Refraction?

When light passes into a different transparent medium:

speed can change

wavelength can change

direction can change

but:

frequency remains constant

This is an important distinction.

The source determines the frequency of the light, so crossing a boundary does not change its frequency.

Frequency and Wavelength

The wave equation is:

v = fλ

where:

v = wave speed

f = frequency

λ = wavelength

When light enters a medium where it travels more slowly:

• v decreases
• f remains constant
• λ decreases

Therefore:

slower light → shorter wavelength in that medium

When light speeds up again:

wavelength increases

Refractive Index

The refractive index, n, describes how much slower light travels through a material compared with its speed in a vacuum.

It is calculated using:

n = c/v

where:

n = refractive index

c = speed of light in vacuum

v = speed of light in the material

Since refractive index is a ratio of two speeds, it has:

no unit

Understanding Refractive Index

A material with a larger refractive index causes light to travel more slowly.

Therefore:

larger n → lower light speed

For example, if:

n = 1.5

then light travels through the material at:

v = c/n

v = (3.00 × 10⁸)/1.5

v = 2.00 × 10⁸ m/s

Light is therefore travelling considerably more slowly than it does in a vacuum.

Typical Refractive Indices

Approximate values for visible light include:

Exact values can depend on wavelength and material composition.

Notice that a higher refractive index corresponds to a lower speed of light in the material.

Worked Example: Speed in Water

The refractive index of water is approximately:

n = 1.33

Use:

n = c/v

Rearrange:

v = c/n

v = (3.00 × 10⁸)/1.33

v ≈ 2.26 × 10⁸ m/s

Light travels through water at approximately:

2.26 × 10⁸ m/s

Optical Density

A material with a higher refractive index is sometimes described as being optically denser.

This does not necessarily mean it has greater mass density.

Optical density refers to how the material affects the speed of light.

Therefore:

optical density and physical density are not the same thing.

Snell's Law

The amount of refraction can be calculated using Snell's law:

n₁ sin θ₁ = n₂ sin θ₂

where:

n₁ = refractive index of the first medium

n₂ = refractive index of the second medium

θ₁ = angle in the first medium

θ₂ = angle in the second medium

All angles are measured from the normal.

Even when a calculation is not required, Snell's law explains why changing refractive index changes the amount of bending.

Worked Example: Air to Glass

Suppose light travels from air into glass.

Use:

n₁ = 1.00

n₂ = 1.50

θ₁ = 30°

Snell's law:

n₁ sin θ₁ = n₂ sin θ₂

1.00 × sin 30° = 1.50 × sin θ₂

0.50 = 1.50 sin θ₂

sin θ₂ = 0.333

Therefore:

θ₂ ≈ 19.5°

The angle decreased from 30° to approximately 19.5°.

The light bent:

toward the normal

as expected.

Refraction in Everyday Life

Refraction produces many familiar effects.

Examples include:

• a straw appearing bent in water
• the bottom of a swimming pool appearing shallower
• objects underwater appearing displaced
• prisms separating colours
• lenses focusing light
• shimmering above hot roads
• atmospheric optical effects

These effects occur because light changes speed as it moves between materials or regions with different optical properties.

 

 

 

7

Apparent Depth

An object underwater can appear closer to the surface than it actually is.

Light travelling from:

water → air

speeds up and bends away from the normal.

Your brain normally assumes that light travelled toward your eyes in a straight line.

As a result, the object appears to be at a different position.

This is why a swimming pool can appear shallower than its true depth.

Lenses

A lens is a transparent optical object with one or more curved surfaces that refracts light.

The two major types are:

• converging lenses
• diverging lenses

Their shapes cause light rays to refract in predictable ways.

Converging Lenses

A converging lens is usually thicker in the centre than at the edges.

It is also commonly called a:

convex lens

Parallel light rays passing through a converging lens are refracted toward the principal axis.

Ideally, they meet at a point called the:

principal focus

or:

focal point

 

 

 

7

Diverging Lenses

A diverging lens is usually thinner in the centre than at the edges.

It is also commonly called a:

concave lens

Parallel rays passing through a diverging lens spread apart.

The rays appear to have originated from a focal point on the same side of the lens as the incoming light.

 

 

 

6

Comparing Converging and Diverging Lenses

Principal Axis

The principal axis is an imaginary line passing through the optical centre of a lens.

Ray diagrams are usually constructed around this line.

Important positions include:

• optical centre
• focal point F
• sometimes 2F

For a thin lens, there is a focal point on each side.

Focal Point

The focal point, F, is a point associated with the refraction of rays through the lens.

For a converging lens:

parallel incoming rays converge at F on the far side.

For a diverging lens:

parallel rays spread apart as though they originated from F on the incoming side.

Focal Length

The focal length, f, is the distance between:

optical centre and focal point

A strongly curved lens generally has greater optical power and a shorter focal length than a less strongly curved lens made from the same material.

The refractive index of the lens material also affects its focusing ability.

Why a Converging Lens Converges Light

A converging lens has curved surfaces.

As light enters and leaves the lens, it refracts at both boundaries.

The combined effect bends rays toward the principal axis.

A ray passing through the centre of a thin lens is often treated as travelling approximately straight in simple ray diagrams.

Parallel rays are brought toward a common focus.

Why a Diverging Lens Diverges Light

The surfaces of a diverging lens cause parallel rays to bend away from the principal axis.

After passing through the lens, the rays spread apart.

If these rays are extended backward, they appear to originate from a common focal point.

Because the rays do not actually meet there, this is a:

virtual focus

Principal Rays for a Converging Lens

Simple lens diagrams use standard rays.

Parallel ray

A ray parallel to the principal axis refracts through the far focal point.

Central ray

A ray passing through the optical centre of a thin lens continues approximately straight.

Focal ray

A ray travelling through the near focal point emerges parallel to the principal axis.

Usually, two correctly drawn rays are sufficient to locate an image.

Constructing a Converging-Lens Ray Diagram

To construct a simple ray diagram:

1. Draw the principal axis.
2. Draw the lens.
3. Mark F on both sides.
4. Mark 2F if needed.
5. Draw the object as an upright arrow.
6. Draw a ray from the top of the object parallel to the axis.
7. Refract that ray through the far F.
8. Draw a second ray through the optical centre.
9. Continue it approximately straight.
10. Locate where the rays intersect.
11. Draw the image at that position.
12. Determine the image's size, orientation, position, and type.

 

 

 

6

Converging Lens: Object Beyond 2F

If an object is placed beyond 2F:

the image forms:

• between F and 2F
• real
• inverted
• smaller

This arrangement is similar to the way some optical systems form reduced real images.

Converging Lens: Object at 2F

If the object is at 2F:

the image forms at approximately 2F on the opposite side.

It is:

• real
• inverted
• same size

Converging Lens: Object Between F and 2F

If the object is between F and 2F:

the image forms beyond 2F.

It is:

• real
• inverted
• enlarged

This arrangement can be useful when an enlarged real image is required.

Converging Lens: Object at F

If the object is at the focal point, emerging rays are approximately parallel.

In the ideal thin-lens model, the image is effectively at a very large distance.

Converging Lens: Object Inside F

If the object is between the lens and F, the refracted rays diverge.

Their backward extensions meet on the same side of the lens as the object.

The image is:

• virtual
• upright
• enlarged

This is how a magnifying glass is used.

Converging Lens Image Summary

The image produced by a converging lens therefore depends strongly on the object's distance from the lens.

Principal Rays for a Diverging Lens

For a diverging lens:

Parallel ray

A ray parallel to the principal axis refracts outward as though it came from the near focal point.

Central ray

A ray passing through the optical centre continues approximately straight.

The refracted rays do not actually meet.

Extend them backward using dashed lines.

The backward extensions locate the virtual image.

Images Formed by Diverging Lenses

For an ordinary real object, a diverging lens produces an image that is:

• virtual
• upright
• smaller
• on the same side of the lens as the object

This is true for ordinary object positions in front of a single diverging lens.

Real and Virtual Images

A real image occurs where light rays actually converge.

A real image can usually be projected onto a screen.

A virtual image occurs where light rays only appear to originate.

The rays do not actually meet at the virtual image location.

Converging lenses can produce:

• real images
• virtual images

Diverging lenses normally produce virtual images for real objects.

Determining Image Characteristics

When describing a lens image, consider:

Type

Real or virtual?

Orientation

Upright or inverted?

Size

Larger, smaller, or the same size?

Position

Where is it relative to the lens and focal points?

These four characteristics provide a useful complete description.

Cameras

A camera uses a converging lens or lens system to form a real image on a sensor.

Light from an object enters the camera.

The lens refracts the rays so that they converge on the image sensor.

The optical image formed on the sensor is:

• real
• typically inverted
• often reduced

Electronic processing then allows the image to be stored and displayed in the familiar orientation.

 

 

 

7

The Human Eye

The human eye also uses refraction.

Light entering the eye is refracted mainly by:

• the cornea
• the lens

The optical system focuses light onto the:

retina

The retina contains light-sensitive cells that convert incoming light into electrical signals.

The brain processes these signals to produce vision.

Focusing in the Eye

The eye must focus light from objects at different distances.

The eye's lens can change shape.

This changes its focusing power.

This process is called:

accommodation

For nearby objects, greater focusing power is generally required.

For distant objects, less focusing power is required.

Corrective Lenses

Some vision problems occur when light does not focus correctly on the retina.

Corrective lenses alter the path of incoming light before it enters the eye.

Different lens types are used for different vision conditions.

Myopia

Myopia, or short-sightedness, occurs when distant objects are focused in front of the retina when the eye is relaxed.

A diverging lens can be used to spread incoming light slightly before it enters the eye.

The eye then focuses the light farther back, onto the retina.

Hyperopia

Hyperopia, or long-sightedness, occurs when the eye would focus light from a near object behind the retina without sufficient accommodation.

A converging lens can help by beginning the convergence before light enters the eye.

This helps the eye focus the image onto the retina.

 

Magnifying Glasses

A magnifying glass uses a:

converging lens

The object is placed:

inside the focal length

The lens produces a:

• virtual
• upright
• enlarged image

This makes small details appear larger.

Microscopes

Optical microscopes use combinations of converging lenses.

A simple compound microscope contains:

• an objective lens
• an eyepiece lens

The lenses work together to produce a highly magnified view of a small object.

Microscopes allow us to observe structures that are too small to see clearly with the unaided eye.

Refracting Telescopes

A refracting telescope uses lenses to collect and focus light from distant objects.

The objective lens gathers light and forms an image.

An eyepiece then allows the observer to view the image at greater angular magnification.

Telescopes demonstrate how refraction can be used to investigate extremely distant objects.

Projectors

A projector uses a converging lens system to produce an enlarged real image on a screen.

Because a screen must receive actual converging light rays, the projected image must be:

real

The positions of the object, lens, and screen are adjusted so that the image is sharply focused.

Refractive Index and Lens Design

The amount of bending produced by a lens depends partly on:

• lens shape
• surface curvature
• refractive index of the lens material
• refractive index of the surrounding medium

A lens made from a material with a different refractive index may require a different shape to achieve the same focal length.

Engineers therefore choose optical materials carefully.

Lenses in Different Surroundings

A lens does not behave only according to its own refractive index.

What matters is also the refractive index of the surrounding medium.

For example, a glass lens behaves differently when surrounded by:

• air
• water
• another transparent material

This is because refraction depends on the change in refractive index across each boundary.

Dispersion in Lenses

The refractive index of a material can vary slightly with wavelength.

Therefore, different colours may refract by slightly different amounts.

This can cause coloured edges in images produced by simple lenses.

This effect is called:

chromatic aberration

Optical engineers can reduce it by combining lenses made from different materials.

Total Internal Reflection

When light travels from a material with higher refractive index toward one with lower refractive index, it bends away from the normal.

At sufficiently large angles, the light may no longer leave the higher-index material.

Instead, it is completely reflected internally.

This is called:

total internal reflection.

It is important in technologies such as:

• optical fibres
• some prisms
• endoscopes
• telecommunications

Optical Fibres

An optical fibre is a thin transparent structure designed to guide light.

Light can be kept inside the fibre through total internal reflection under appropriate conditions.

Optical fibres are used in:

• internet communication
• telephone networks
• medical endoscopes
• sensors

Although an optical fibre is not simply a lens, it demonstrates how refractive index and refraction principles can be engineered to control light.

 

 

 

6

Lens Power

The strength of a lens can be described by its optical power.

Lens power is related to focal length:

P = 1/f

when f is measured in metres.

The unit of lens power is the:

dioptre (D)

For example, a converging lens with:

f = 0.50 m

has:

P = 1/0.50

P = +2.0 D

Converging lenses have positive power.

Diverging lenses have negative power.

Worked Example: Lens Power

A converging lens has:

f = 0.25 m

Calculate its power.

Use:

P = 1/f

P = 1/0.25

P = +4.0 D

The positive sign indicates a converging lens.

Comparing Mirrors and Lenses

Mirrors and lenses can both control light, but they operate differently.

Mirrors

primarily use:

reflection

Lenses

primarily use:

refraction

Both can:

• converge light
• diverge light
• form images
• magnify objects
• be used in optical instruments

This is why similar ray-diagram ideas appear in both topics.

A Complete Ray-Diagram Example

Suppose an object is placed beyond 2F in front of a converging lens.

Draw a ray from the top of the object:

parallel to the principal axis

After passing through the lens, it refracts through the far focal point.

Draw another ray:

through the optical centre

It continues approximately straight.

The two rays intersect on the opposite side of the lens between F and 2F.

Therefore, the image is:

• real
• inverted
• smaller
• between F and 2F

The ray diagram allows all four image characteristics to be determined.

Choosing the Correct Lens

When given an unfamiliar lens problem, first ask:

Does the lens bring parallel rays together?

→ converging lens

Does the lens spread parallel rays apart?

→ diverging lens

Then determine:

• object position
• focal point
• principal axis
• ray directions
• image location

Finally describe:

• type
• orientation
• size
• position

A Reliable Strategy for Refraction Problems

When light crosses a boundary:

1. Identify the two media.
2. Draw the boundary.
3. Draw the normal.
4. Identify the incident ray.
5. Determine whether light speeds up or slows down.
6. If it slows, predict bending toward the normal.
7. If it speeds up, predict bending away from the normal.
8. Remember that frequency remains constant.
9. Use n = c/v if speed or refractive index is required.
10. Use Snell's law if angles must be calculated.
11. Check that all angles are measured from the normal.
12. Interpret the result physically.

A Reliable Strategy for Lens Ray Diagrams

For a simple lens diagram:

1. Draw the principal axis.
2. Draw the lens.
3. Mark F on both sides.
4. Mark 2F when useful.
5. Draw the object.
6. Start rays from the top of the object.
7. Use a parallel ray.
8. Use a central ray or focal ray.
9. Draw the refracted rays accurately.
10. Extend rays backward with dashed lines if necessary.
11. Locate the image.
12. State whether it is real or virtual.
13. State whether it is upright or inverted.
14. Compare its size with the object.
15. Check whether the result makes sense for that lens type and object position.

Common Mistakes

Thinking refraction means reflection

Reflection sends light back from a boundary.

Refraction involves light passing into another medium and changing speed, often changing direction.

Measuring angles from the surface

Refraction angles are measured from the normal.

Thinking light always bends when entering another material

A ray travelling along the normal changes speed but does not change direction.

Thinking light bends toward the normal whenever it enters any new medium

It bends toward the normal when it enters a medium where it travels more slowly.

Thinking frequency changes during refraction

Frequency remains constant across the boundary.

Thinking wavelength stays constant

If wave speed changes while frequency remains constant, wavelength changes.

Thinking higher refractive index means faster light

It means the opposite:

higher n → lower speed

Confusing converging and diverging lenses

A converging lens brings parallel rays together.

A diverging lens spreads parallel rays apart.

Thinking all converging-lens images are real

A converging lens produces a virtual image when the object is inside its focal length.

Thinking a magnifying glass forms an enlarged real image on the object side

When used normally, it forms an enlarged virtual image.

Drawing virtual rays as actual light rays

Backward extensions used to locate virtual images should be shown as dashed lines.

Thinking optical density is the same as mass density

They describe different physical properties.

Key Terms

Refraction — change in direction of light associated with a change in speed as it enters a different medium.

Incident ray — incoming light ray approaching a boundary.

Refracted ray — light ray travelling through the second medium after crossing a boundary.

Normal — imaginary line perpendicular to a boundary at the point where a ray strikes it.

Angle of incidence — angle between the incident ray and the normal.

Angle of refraction — angle between the refracted ray and the normal.

Refractive index — measure of how much light slows in a material compared with its speed in vacuum.

Optical density — description related to how strongly a material reduces the speed of light.

Snell's law — relationship connecting refractive indices and angles of incidence and refraction.

Lens — transparent optical object that refracts light using curved surfaces.

Converging lens — lens that causes parallel rays to converge; commonly a convex lens.

Diverging lens — lens that causes parallel rays to diverge; commonly a concave lens.

Principal axis — reference line through the optical centre of a lens.

Optical centre — central reference point of a thin lens through which a ray is approximated as travelling straight.

Focal point (F) — point where parallel rays converge or from which diverging rays appear to originate.

Focal length (f) — distance between the optical centre and focal point.

Real image — image formed where actual light rays converge.

Virtual image — image formed where light rays appear to originate.

Lens power — measure of the focusing strength of a lens.

Dioptre (D) — unit of lens power.

Accommodation — adjustment of the eye's focusing power to view objects at different distances.

Myopia — vision condition in which distant objects are focused in front of the retina without correction.

Hyperopia — vision condition in which near objects would be focused behind the retina without sufficient accommodation.

Total internal reflection — complete reflection of light within a higher-index material under suitable conditions.

Chromatic aberration — colour distortion caused by different wavelengths being refracted by different amounts.

Key Takeaways

• Refraction occurs because light changes speed when it enters a different medium.
• Light bends toward the normal when it enters a medium where it travels more slowly.
• Light bends away from the normal when it enters a medium where it travels faster.
• A ray travelling along the normal does not change direction even though its speed may change.
• Angles of incidence and refraction are measured from the normal.
• During refraction, frequency remains constant.
• If speed changes, wavelength changes.
• Refractive index is calculated using n = c/v.
• A larger refractive index means a lower speed of light in the material.
• Snell's law relates refractive index to the angles of incidence and refraction.
• Everyday refraction explains why underwater objects can appear displaced.
• Lenses control light through refraction.
• Converging lenses bring parallel rays toward a focal point.
• Diverging lenses spread parallel rays apart.
• Converging lenses can produce real or virtual images depending on object position.
• Diverging lenses normally produce virtual, upright, reduced images for real objects.
• Ray diagrams can determine image position, type, orientation, and size.
• Magnifying glasses use converging lenses with the object inside the focal length.
• Cameras use lenses to form real images on sensors.
• The human eye uses refraction to focus light onto the retina.
• Diverging and converging corrective lenses can help correct different vision problems.
• Microscopes and refracting telescopes use combinations of lenses.
• Refractive index and lens curvature affect focusing strength.
• Total internal reflection allows light to be guided through optical fibres.
• Refraction and lenses are central to vision, medicine, communication, photography, astronomy, and many other optical technologies.

Check Your Understanding

1. Explain why light can change direction when it enters a different transparent medium.
2. Define the angle of incidence and angle of refraction. From which line are both angles measured?
3. Light travels from air into glass at an angle to the normal. Explain what happens to its speed and direction.
4. Light travels from glass into air at an angle below the critical angle. Explain why it bends away from the normal.
5. A light ray travels directly along the normal from air into water. Its speed changes. Explain why its direction does not change.
6. Describe what happens to the speed, frequency, and wavelength of light when it enters a material where it travels more slowly.
7. A transparent material has a refractive index of 1.50. Calculate the speed of light in the material using c = 3.00 × 10⁸ m/s.
8. Explain the difference between a converging lens and a diverging lens in terms of shape and their effect on parallel light rays.
9. Describe how to construct a simple ray diagram for a converging lens.
10. An object is placed beyond 2F in front of a converging lens. Describe the position, type, orientation, and size of the image.
11. An object is placed between F and a converging lens. Describe the resulting image and explain why this arrangement is useful in a magnifying glass.
12. Describe the image normally produced by a diverging lens for a real object.
13. Explain how a camera and the human eye both use refraction and converging optical systems to form images.
14. Explain why refractive index is important when engineers design lenses for cameras, microscopes, telescopes, glasses, or other optical instruments.
15. A student says, "A lens bends light simply because its surfaces are curved." Improve this explanation by describing the roles of changing light speed, refractive index, refraction at boundaries, and lens shape.