Welcome to Waves: Refraction and Total Internal Reflection!

Hello future physicist! This chapter is all about how light behaves when it moves from one material (or medium) to another, like from air into water. It’s an essential part of the 'Waves' section because it explains everything from why a straw looks bent in a glass of water to how modern internet signals travel through tiny cables!

Don't worry if these concepts seem tricky at first; we will break them down into simple, easy-to-understand steps using analogies you already know.

1. Understanding Refraction

What is Refraction?

Refraction is the change in direction of a wave (like light) as it passes from one medium to another, caused by the change in the wave's speed.

When light travels from air into glass, it slows down. This change in speed causes the light ray to bend. If light speed didn't change, there would be no refraction!

Analogy: The Marching Band

Imagine a marching band marching quickly across a smooth road (fast medium, like air). They then try to march diagonally onto a grassy field (slow medium, like glass).

  • As the first row of marchers hits the grass, they slow down.
  • The marchers still on the road keep moving fast.
  • Because one side of the line is moving slower than the other, the whole line swings around (changes direction). This "swing" is refraction!

Key Terms in Refraction

When drawing diagrams, you need to know these three key lines and angles:

  • Normal: This is an imaginary line drawn perpendicular (at 90°) to the surface where the light enters the new material. All angles are measured from the Normal.
  • Angle of Incidence (\(i\)): The angle between the incoming light ray and the Normal.
  • Angle of Refraction (\(r\)): The angle between the refracted (bent) light ray and the Normal.

The Direction of Bending

The direction light bends depends on whether it speeds up or slows down:

Case 1: Going Slower (Air to Glass)

When light goes from a less dense medium (where it is fast) to a denser medium (where it is slow, e.g., air to water):

  • The light ray bends TOWARDS the Normal.
  • This means the angle of refraction (\(r\)) will be smaller than the angle of incidence (\(i\)).

Case 2: Going Faster (Glass to Air)

When light goes from a denser medium (where it is slow) to a less dense medium (where it is fast, e.g., water to air):

  • The light ray bends AWAY from the Normal.
  • This means the angle of refraction (\(r\)) will be larger than the angle of incidence (\(i\)).
Memory Aid: S-T-A-F

Use this simple trick to remember the direction:

Slow Towards (Going into a slower medium, it bends Towards the Normal).
Away Fast (Going into a faster medium, it bends Away from the Normal).

Quick Review: Refraction

Refraction happens because light speed changes. If light moves from air (fast) to glass (slow), it bends towards the Normal.

2. The Refractive Index (\(n\))

What is the Refractive Index?

Different materials slow light down by different amounts. The refractive index (\(n\)) is a number that tells us exactly how much a material slows light down compared to its speed in a vacuum (or air).

A high refractive index (like for diamond, \(n \approx 2.4\)) means the light slows down a lot and bends significantly. A low refractive index (like air, \(n \approx 1.00\)) means little bending.

The Refractive Index Formula (Speed Definition)

The refractive index (\(n\)) is defined by the ratio of the speed of light in a vacuum (\(c\)) to the speed of light in the medium (\(v\)).

$$n = \frac{\text{Speed of light in vacuum}}{\text{Speed of light in medium}}$$

Or, using symbols:

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

Important Point: Since the speed of light in the medium (\(v\)) is always less than the speed of light in a vacuum (\(c\)), the refractive index (\(n\)) is always greater than 1.

Did you know?

When light enters water, it travels about 25% slower than it does in the air! This is why objects underwater look closer and larger than they actually are.

3. Critical Angle and Total Internal Reflection (TIR)

Refraction usually involves light passing through a boundary, but under specific conditions, light can be reflected completely back into the material it came from. This is called Total Internal Reflection (TIR).

The Critical Angle (\(c\))

Imagine light traveling from a dense medium (like water) into a less dense medium (like air).

As you increase the angle of incidence (\(i\)), the angle of refraction (\(r\)) gets larger and larger (remember: Away Fast!).

The Critical Angle (\(c\)) is the specific angle of incidence that causes the angle of refraction (\(r\)) to be exactly 90°.

  • At the critical angle, the refracted ray travels right along the boundary surface (grazing the surface).

Conditions for Total Internal Reflection (TIR)

TIR can only happen if two essential conditions are met:

  1. The light must be traveling from a denser medium to a less dense medium (e.g., Glass to Air).
  2. The Angle of Incidence (\(i\)) must be greater than the Critical Angle (\(c\)) of the material.

When these two conditions are met, no refraction occurs. Instead, 100% of the light is reflected back into the dense medium. This is TIR!

Common Mistake Alert!

A common mistake is thinking TIR can happen when light moves from air to glass. It CANNOT. Light must be trying to speed up (denser to less dense) for TIR to be possible.

Calculating the Critical Angle

The critical angle (\(c\)) is related to the refractive index (\(n\)) of the denser material by the following formula:

$$\sin c = \frac{1}{n}$$

If you know the refractive index (\(n\)), you can calculate the critical angle (\(c\)). Conversely, if you measure the critical angle, you can find the refractive index.

Key Takeaway: TIR Summary

TIR is perfect reflection (100%). It only happens when light tries to leave a slow material (dense) but hits the boundary at an angle too wide (larger than the critical angle).

4. Applications of Total Internal Reflection

TIR is not just a laboratory curiosity; it is a fundamental principle used in many modern technologies because it provides an almost perfect, lossless way to guide light.

Optical Fibres

Optical fibres are tiny, hair-thin strands of high-quality glass or plastic. They are essential for high-speed internet, phone lines, and even medical imaging (endoscopes).

How do they work?

1. Light signals (pulses) are sent into the core of the fibre (the denser medium).

2. The core is surrounded by a layer called the cladding, which has a much lower refractive index (the less dense medium).

3. The light hits the boundary between the core and the cladding at an angle that is always greater than the critical angle.

4. Because the angle is too large, the light undergoes Total Internal Reflection (TIR) and bounces perfectly back into the core, continuing down the length of the fibre, even around corners!

Reflecting Prisms

TIR is used in glass prisms found in high-quality binoculars, periscopes, and cameras.

  • A glass prism is shaped such that light entering it hits the internal surfaces at 45°.
  • Since the critical angle for typical glass is around 42°, the light hits the surface at an angle greater than \(c\).
  • This results in 90° or 180° reflection, which is much more efficient and clearer than using a traditional silvered mirror.

The efficiency of TIR makes it invaluable – no energy is lost as the light signal bounces, meaning the signal can travel huge distances without needing to be amplified as often.