Physics (9203) | Refraction and total internal reflection

Welcome to the World of Refraction!

Hello future Physicists! This chapter, "Refraction and Total Internal Reflection," is one of the most exciting parts of the "Waves" section. Why? Because it explains why things look bent in water, how diamonds sparkle, and how the internet travels through tiny glass threads!

Don't worry if these ideas seem abstract; we will break them down step-by-step using everyday examples. Let's dive in!

1. Understanding Refraction: The Bending of Light

What is Refraction?

Refraction is defined as the change in direction of a wave (in our case, light) as it passes from one transparent medium into another, due to the change in its speed.

Think about looking at a spoon sitting in a glass of water. The spoon looks broken or bent at the surface of the water. This optical illusion is caused by refraction!

Why Does Light Bend? (The Cause)

Light travels at different speeds in different materials (media). It travels fastest in a vacuum (or air) and slower in denser materials like water or glass.

Analogy: Imagine pushing a shopping trolley from a smooth tiled floor (air, fast) onto thick grass (glass, slow). If you push the trolley at an angle, the wheel that hits the grass first slows down, causing the trolley to swivel and change direction. Light does the exact same thing!

Key Terms You Must Know

To study refraction accurately, we use ray diagrams and specific terms:

• Normal: This is an imaginary line drawn perpendicular (at 90°) to the boundary between the two media. All angles are measured from the Normal.
• Angle of incidence (\(i\)): The angle between the incident ray and the Normal.
• Angle of refraction (\(r\)): The angle between the refracted ray and the Normal.

2. Rules of Bending: Drawing Ray Diagrams

The direction light bends depends entirely on whether it is speeding up or slowing down.

Rule 1: Less Dense (Air) to More Dense (Glass/Water)

When light moves from a material where it is fast (like air) into a material where it is slow (like glass):

• The light slows down.
• The ray bends TOWARDS the Normal.
• This means the angle of incidence (\(i\)) is greater than the angle of refraction (\(r\)).

Rule 2: More Dense (Glass/Water) to Less Dense (Air)

When light moves from a material where it is slow (like glass) into a material where it is fast (like air):

• The light speeds up.
• The ray bends AWAY from the Normal.
• This means the angle of incidence (\(i\)) is less than the angle of refraction (\(r\)).

Memory Aid: T.A.S.T.

Don't worry about remembering which angle is bigger. Use this simple guide:

Towards = Slower (More dense)
Away = Faster (Less dense)

3. The Refractive Index (\(n\)) and Snell's Law

Every transparent material has a unique measure of how much it slows down light and how much it refracts the light. This measure is called the Refractive Index (\(n\)).

The higher the refractive index, the more the material slows down light, and the more it bends the light ray.

Calculating Refractive Index (The definition using speed)

The refractive index (\(n\)) is defined using the ratio of the speed of light in a vacuum (or air) to the speed of light in the specific medium:

$$n = \frac{\text{Speed of light in vacuum (c)}}{\text{Speed of light in medium (v)}}$$

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

Since the speed of light in the medium (v) must always be slower than c, the value of \(n\) is always greater than 1 (except for air, where it is very close to 1).

Snell’s Law (The definition using angles)

For any given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. This constant is the refractive index (\(n\)).

$$n = \frac{\sin i}{\sin r}$$

Step-by-Step Calculation Tip

When solving problems using Snell's Law, always ensure your calculator is in "DEG" (degrees) mode!

Common Mistake to Avoid: Always measure \(i\) and \(r\) from the Normal, not the surface boundary.

4. Total Internal Reflection (TIR)

When light travels from a dense medium (like glass) to a less dense medium (like air), we saw that it bends AWAY from the Normal. But what happens if we increase the angle of incidence (\(i\)) too much?

Scenario 1: Refraction

If \(i\) is small, the light refracts and passes into the air, bending away from the normal.

Scenario 2: The Critical Angle (\(c\))

As we increase the angle \(i\), the refracted ray in the air gets closer and closer to the boundary surface. When the angle of refraction (\(r\)) reaches exactly 90°, the angle of incidence that causes this is called the Critical Angle (\(c\)).

At the Critical Angle, the light travels along the boundary surface—it doesn't actually escape the denser medium.

Scenario 3: Total Internal Reflection (TIR)

If the angle of incidence (\(i\)) is increased to be greater than the Critical Angle (\(c\)), the light ray cannot escape the denser medium at all. Instead, it is reflected entirely back into the denser medium. This is called Total Internal Reflection (TIR).

Conditions for Total Internal Reflection (Crucial!)

TIR can only occur if two conditions are met:

1. The light must be travelling from a denser medium (higher \(n\)) to a less dense medium (lower \(n\)).
2. The angle of incidence (\(i\)) must be greater than the Critical Angle (\(c\)).

The Relationship between Refractive Index and Critical Angle

The critical angle (\(c\)) is directly related to the refractive index (\(n\)) of the material. Since the angle of refraction at the critical angle is 90° (\(\sin 90^\circ = 1\)):

$$n = \frac{\sin i}{\sin r} \implies n = \frac{\sin c}{\sin 90^\circ}$$

This simplifies to:

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

Or, rearranging to find the critical angle:

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

5. Applications of Total Internal Reflection

Total Internal Reflection is not just a physics concept; it powers much of our modern world!

Application 1: Optical Fibres (Light Pipes)

Optical Fibres are thin strands of very pure glass or plastic used to transmit light (and therefore information, like data, phone calls, and TV signals) over long distances.

• A fibre consists of a dense core (high \(n\)) surrounded by a thinner, less dense coating called the cladding (low \(n\)).
• Light enters the core at a shallow angle.
• Because the light travels from a dense core to a less dense cladding, and the angle of incidence is greater than the critical angle, the light experiences TIR.
• The light continually bounces off the inner walls of the core without escaping, transmitting data efficiently and quickly.

Did you know? Modern internet relies almost entirely on optical fibres running under the oceans and land!

Application 2: Prisms in Optical Instruments

Glass prisms are often used in periscopes and binoculars instead of mirrors because TIR provides a perfect, 100% reflection (no energy is lost) and does not tarnish over time.

A right-angled prism can be used:

1. To turn a beam of light through 90° (using one TIR reflection).
2. To turn a beam of light through 180° (using two sequential TIR reflections).

The refractive index of glass (about 1.5) means its critical angle is usually around 42°. In a right-angled prism, light hitting the diagonal face will hit it at 45°, which is greater than 42°, ensuring TIR occurs.