Geometrical Optics (Grade 11 NSC Matric Physical Sciences): Revision Notes

Critical Angles and Total Internal Reflection

What is total internal reflection?

When you experiment with light and glass blocks, you might notice something interesting happens at certain angles. Sometimes, instead of the light passing through and bending (refracting), it gets completely reflected back into the material. This phenomenon is called total internal reflection.

Total internal reflection occurs when light travelling through an optically denser medium hits the boundary with a less dense medium, but instead of passing through, the entire light ray reflects back into the original medium.

Understanding the critical angle

Before total internal reflection can happen, there's a special angle we need to understand. As we increase the angle of incidence gradually, we reach a point where the refracted ray travels exactly along the boundary between the two materials - this means the angle of refraction becomes 90°. This special angle of incidence is called the critical angle.

Conditions for total internal reflection

For total internal reflection to happen, two conditions must be met:

When the angle of incidence exceeds the critical angle, no refracted ray emerges from the medium. Instead, the light ray is completely reflected back into the denser medium.

Calculating the critical angle

Instead of always measuring critical angles experimentally, we can calculate them using Snell's Law. Remember that Snell's Law states:

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

Where:

• $n_1$ is the refractive index of the first material
• $n_2$ is the refractive index of the second material
• $\theta_1$ is the angle of incidence
• $\theta_2$ is the angle of refraction

At the critical angle, we know that:

• $\theta_1 = \theta_c$ (the critical angle)
• $\theta_2 = 90°$

Since $\sin 90° = 1$, we can write: $n_1 \sin \theta_c = n_2 \times 1$

Solving for the critical angle: $\sin \theta_c = \frac{n_2}{n_1}$

Therefore: $\theta_c = \sin^{-1}\left(\frac{n_2}{n_1}\right)$

Worked example: calculating critical angle

Understanding different scenarios

Let's examine what happens at different angles when light travels from water to air.

The table below shows how the angle of refraction changes with the angle of incidence:

Angle of incidence	Angle of refraction
0°	0.00°
30°	22.1°
45°	32.1°
48.8°	90°
50°	No refraction (total internal reflection)

Practical experiment: finding the critical angle

Aim: To determine the critical angle for a rectangular glass block.

Apparatus: Rectangular glass block, ray box, 360° protractor, paper, pencil, ruler

Method:

1. Place the glass block on paper and trace its outline
2. Turn on the ray box and direct light into the side of the glass block
3. Adjust the angle until you see the refracted ray travelling along the top edge of the block (angle of refraction = 90°)
4. Mark the points where light enters and exits the block
5. Remove the glass block and draw a line between the marked points
6. Use the protractor to measure the angle of incidence - this is your critical angle

Applications: fibre optics

Total internal reflection has many practical applications, with fibre optics being one of the most important. Optical fibres are thin strands of glass or plastic used to transmit light signals over long distances.

Structure of optical fibres

An optical fibre consists of two main parts:

• Inner core: The central region through which light travels
• Cladding: The outer layer with a lower refractive index than the core

How fibre optics work

Light signals enter the fibre at angles greater than the critical angle. As the light travels down the fibre, it repeatedly undergoes total internal reflection at the core-cladding boundary. This keeps the light trapped inside the core, allowing it to travel long distances with minimal loss.

Applications of fibre optics

Telecommunications: Optical fibres can transmit thousands of signals simultaneously over long distances. The information travels at the speed of light, making fibre optic cables much faster than traditional copper cables.

Medicine: Endoscopes use optical fibres to allow doctors to see inside the human body. Light travels down one set of fibres to illuminate internal organs, while another set carries the reflected light back to create an image.