Refraction of Light - Critical Angle

This section explains the concept of the critical angle, a key aspect of light refraction.

What is Refraction?

Refraction is the bending of light as it passes from one transparent medium to another. This bending occurs because light travels at different speeds in different media.

Critical Angle Explained

The critical angle is the angle of incidence at which the angle of refraction is 90 degrees. When the angle of incidence exceeds the critical angle, total internal reflection occurs.

Mathematical Definition

The critical angle (θ_c) can be calculated using Snell's Law:

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

At the critical angle, θ₂ = 90° (or $\frac{\pi}{2}$ radians). Therefore, we have:

$n_1 \sin{\theta_1} = n_2 \sin{90°}$

$n_1 \sin{\theta_1} = n_2 \times 1$

$n_1 \sin{\theta_1} = n_2$$

So, the critical angle is:

$$\theta_c = \arcsin\left(\frac{n_2}{n_1}\right)$$

where:

• $n_1$ is the refractive index of the first medium (the medium light is coming from).
• $n_2$ is the refractive index of the second medium (the medium light is entering).

Conditions for Total Internal Reflection

Total internal reflection occurs when the angle of incidence (θ₁) is greater than the critical angle (θ_c). This means that light entering the second medium is incident on the boundary at an angle greater than the critical angle, and all of the light is reflected back into the first medium.

Table Summary

Concept	Definition
Critical Angle (θc)	The angle of incidence at which the angle of refraction is 90 degrees.
Formula	$$\theta_c = \arcsin\left(\frac{n_2}{n_1}\right)$$
Total Internal Reflection	Occurs when the angle of incidence exceeds the critical angle.

Importance of Critical Angle

The critical angle is important in applications such as:

• Optical fibers: Used to guide light over long distances by repeatedly reflecting it internally.
• Prisms: Used to disperse white light into its constituent colors.
• Searchlights: Used to create a powerful beam of light by reflecting light internally.