first

Reflection can also occur when waves travel from one material into another and their speed changes. When a wave enters a different medium, such as light moving from air into water or sound travelling through different materials, its speed may change due to differences in density or stiffness of the medium. This change in wave speed can cause part or all of the wave to be reflected at the boundary between the two materials.

Understanding wave properties and how waves reflect helps explain many everyday phenomena, such as echoes, reflections in mirrors, and the behaviour of light and sound when they travel through different substances.

Worksheets: Wave Properties 3, 1, 2

To determine the speed of light in a medium, we usually use the concept of refractive index. The refractive index tells us how much light slows down when it enters a material.

Relationship Between Speed and Refractive Index

The key equation is:

$n = \frac{c}{v}$

n=vc​

Where:

• $n$

  n = refractive index of the medium

• $c$

  c = speed of light in a vacuum (

  $3.00 \times 10^8 \, \text{m/s}$

  3.00×108m/s)

• $v$

  v = speed of light in the medium

Rearranging the equation to find the speed in the medium:

$v = \frac{c}{n}$

v=nc​

Example

Suppose light enters water, which has a refractive index of about 1.33.

$v = \frac{3.00 \times 10^8}{1.33}$

v=1.333.00×108​

$v \approx 2.26 \times 10^8 \, \text{m/s}$

v≈2.26×108m/s

So the speed of light in water is approximately:

$2.26 \times 10^8 \, \text{m/s}$

2.26×108m/s

Another Example: Glass

Typical refractive index of glass ≈ 1.5

$v = \frac{3.00 \times 10^8}{1.5}$

v=1.53.00×108​

$v = 2.00 \times 10^8 \, \text{m/s}$

v=2.00×108m/s

Important Idea

When light enters a medium:

• Speed decreases

• Frequency stays the same

• Wavelength decreases

This change in speed is what causes refraction (bending of light).

Use the  PHeT and 

1. Set n₁ = 1.60
2. For the second material, choose "Mystery B"

Summative Lab Report:

1. Review the Lab Report Overview
2. Review your Formative Lab Feedback
3. Before you begin the lab, make a hypothesis about n₂.

When light travels from one material (medium) to another, its speed changes, and this usually causes the light to change direction. This process is called refraction. Refraction occurs because light travels at different speeds in different media, such as air, water, or glass. When light enters a new medium at an angle (not along the normal), the change in speed causes the light ray to bend at the boundary between the two media.

The refractive index of a material describes how much the material slows light down compared to its speed in a vacuum. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material. A higher refractive index means light travels more slowly in that medium and bends more when entering it. For example, glass has a higher refractive index than air, so light slows down and changes direction more when entering glass from air.

The relationship between the angles and refractive indices when light passes between two media is described by Snell’s Law:

$n_1 \sin \theta_1 = n_2 \sin \theta_2$

n1​sinθ1​=n2​sinθ2​

where

$n_1$

n1​ and

$n_2$

n2​ are the refractive indices of the first and second media,

$\theta_1$

θ1​ is the angle of incidence, and

$\theta_2$

θ2​ is the angle of refraction. This law can be used to calculate unknown angles or refractive indices when light passes from one medium to another.

Light does not always bend in the same way. When light enters a medium with a higher optical density (higher refractive index), such as from air into glass or water, it slows down and bends toward the normal. The angle of refraction is smaller than the angle of incidence. When light enters a medium with a lower optical density (lower refractive index), such as from glass into air, it speeds up and bends away from the normal, making the angle of refraction larger than the angle of incidence.

Being able to predict how light bends requires comparing the refractive indices of the two media. If the second medium has a larger refractive index, expect bending toward the normal; if it has a smaller refractive index, expect bending away from the normal. This understanding, together with Snell’s Law, allows accurate prediction and calculation of the path of light as it moves between different materials.

Worksheet: Refraction 1

Total Internal Reflection (TIR): Conditions and Applications 

Total Internal Reflection (TIR) is a special optical phenomenon where a light ray completely reflects inside a medium instead of refracting into another medium. This principle is widely used in fiber optics, diamonds, and mirages.

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What is Total Internal Reflection?

TIR occurs when:

1. Light travels from a denser medium (higher refractive index) to a less dense medium (lower refractive index).
2. The angle of incidence is greater than the critical angle ($\theta_c$​), so no refraction occurs—only reflection.

Example:

• A laser inside water can reflect completely at the water-air boundary.
• Diamonds sparkle because of TIR inside them.

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Conditions for Total Internal Reflection

(a) Light Moves from a Denser to a Less Dense Medium

• TIR occurs only if$n_1 > n_2$​ (higher to lower refractive index).
• Examples:
  • Water to Air ($n_{\text{water}} = 1.33$n,$n_{\text{air}} = 1.0003$)
  • Glass to Air ($n_{\text{glass}} = 1.5$,$n_{\text{air}} = 1.0003$)
  • Diamond to Air ($n_{\text{diamond}} = 2.42$,$n_{\text{air}} = 1.0003$)

(b) The Angle of Incidence Exceeds the Critical Angle

• The critical angle ($\theta_c$​) is the angle where light just refracts along the boundary ($90^\circ$).
• If$\theta_i > \theta_c$​, TIR occurs.

$\sin \theta_c = \frac{n_2}{n_1}$

where:

• $n_1$​ = refractive index of the denser medium.
• $n_2$​ = refractive index of the less dense medium.

Example Calculation (Water to Air)

$\sin \theta_c = \frac{n_2}{n_1} = \frac{1.0003}{1.33}$

​

$\theta_c = \sin^{-1} (0.752) = 48.75^\circ$

If light hits at more than

$48.75^\circ$

, total internal reflection occurs.

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3. Applications of Total Internal Reflection

(a) Optical Fibers & Internet Cables 

• TIR is used in fiber optics to transmit light signals over long distances.
• Light reflects entirely inside the fiber with almost no loss.
• Used in:
  • High-speed internet & telecommunications
  • Endoscopes in medical imaging
  • Military communication systems

Example:

• Fiber optic cables send phone & internet signals by bouncing light inside a glass fiber.

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(b) Diamonds & Jewelry 

• Diamonds sparkle intensely due to their high refractive index ($n = 2.42$).
• The critical angle is very small ($\theta_c \approx 24^\circ$θ), so light is trapped and reflected multiple times before escaping.

Result:

• More internal reflections = Brighter sparkle in diamonds.

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(c) Mirage Formation & Atmospheric Refraction 

• Mirages occur in deserts & hot roads due to TIR of light in air layers.
• On hot surfaces, warm air has a lower refractive index than cool air above it.
• Light bends and reflects back upwards, creating an illusion of water.

Example:

• Seeing a "water puddle" on a hot highway that disappears when approached.

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(d) Periscopes & Binoculars 

• Periscopes use TIR mirrors to change light direction.
• Binoculars & telescopes use prisms with TIR to enhance image brightness.

Example:

• Submarines use periscopes with TIR to see above water.

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4. Summary of Total Internal Reflection

Condition	Requirement
Medium Change	Light must travel from denser to less dense medium ($n_1 > n_2$​).
Angle of Incidence	Must be greater than the critical angle ($\theta_i > \theta_c$​).
Critical Angle Formula	$\sin \theta_c = \frac{n_2}{n_1}$

Application	How TIR is Used
Optical Fibers	Data transmission via light reflection.
Diamonds	Internal reflections create sparkle.
Mirages	Light bends due to hot/cold air layers.
Periscopes & Binoculars	TIR redirects light for vision enhancement.

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Key Takeaways

• Total Internal Reflection keeps light trapped inside a medium, leading to practical applications in optics and technology.
• Used in fiber optics, diamonds, mirages, and optical instruments like periscopes.
• Critical angle calculations determine when TIR occurs.
• TIR is the secret behind high-speed internet, sparkling diamonds, and mirages! 

Activities:

• Demonstrate total internal reflection with a laser and a water-filled tube.
• Research project on fiber optics.

Assessment: Reflection essay on the importance of total internal reflection.