Light Waves
2. Reflection and Mirrors
Learning outcomes
- I can state the law of reflection.
- I can construct ray diagrams for plane mirrors.
- I can distinguish between plane, concave, and convex mirrors.
- I can determine image characteristics formed by mirrors.
- I can identify applications of mirrors.
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.
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:
- Draw the mirror as a straight line.
- Draw the object in front of the mirror.
- Select a point on the object, usually its top.
- Draw at least two rays from that point toward the mirror.
- At each point of reflection, draw or imagine the normal.
- Reflect each ray using θᵢ = θᵣ.
- Extend the reflected rays backward behind the mirror using dashed lines.
- Locate the point where the backward extensions meet.
- Repeat if necessary for another point on the object.
- Draw the virtual image.
The dashed lines represent where the reflected rays appear to originate.
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.
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.
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
| Object Position | Image Position | Type | Orientation | Size |
|---|---|---|---|---|
| Beyond C | Between C and F | Real | Inverted | Smaller |
| At C | At C | Real | Inverted | Same |
| Between C and F | Beyond C | Real | Inverted | Larger |
| At F | Very far away | Limiting case | Inverted | Very large |
| Between F and mirror | Behind mirror | Virtual | Upright | Larger |
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.
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
| Property | Plane Mirror | Concave Mirror | Convex Mirror |
|---|---|---|---|
| Surface | Flat | Curves inward | Curves outward |
| Effect on parallel rays | Remain organized | Converge | Diverge |
| Image type | Virtual | Real or virtual | Virtual |
| Image orientation | Upright | Inverted or upright | Upright |
| Image size | Same | Smaller, same, or larger | Smaller |
| Field of view | Moderate | Usually narrower | Wide |
| Typical use | Household mirror | Magnification/focusing | Wide-angle viewing |
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:
- strikes the upper mirror
- reflects downward
- strikes the lower mirror
- 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
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.
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:
- a ray parallel to the principal axis, which reflects through F
- 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:
- draw a ray parallel to the principal axis
- reflect it so that it appears to originate from F behind the mirror
- draw another suitable ray
- 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:
- Identify the reflecting surface.
- Locate the point where the incident ray strikes.
- Draw the normal perpendicular to the surface.
- Identify the angle of incidence.
- Make sure the angle is measured from the normal.
- Apply θᵢ = θᵣ.
- Draw the reflected ray.
- If constructing an image, use at least two rays.
- Extend reflected rays backward with dashed lines if locating a virtual image.
- Identify the image position.
- State whether the image is real or virtual.
- State whether it is upright or inverted.
- Compare its size with the object.
- 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
- State the law of reflection.
- Define the incident ray, reflected ray, and normal.
- A ray strikes a mirror at 28° to the normal. Determine the angle of reflection.
- A ray makes an angle of 25° with the mirror surface. Determine its angle of incidence and angle of reflection.
- Explain why a rough wall can still obey the law of reflection even though it does not produce a clear image.
- Describe the four main characteristics of an image produced by a plane mirror.
- 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?
- Describe how to construct a ray diagram for an object viewed in a plane mirror.
- Explain the difference between a real image and a virtual image.
- An object is placed beyond C in front of a concave mirror. Describe the image's position, type, orientation, and relative size.
- 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.
- Describe the image normally produced by a convex mirror and explain why convex mirrors are useful for vehicle and security applications.
- Compare plane, concave, and convex mirrors in terms of shape, effect on reflected rays, and typical image characteristics.
- 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.
- 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.