Solved Examples on Total Internal Reflection

Example 1: If the critical angle for total internal reflection from a medium to vacuum is 45°. Determine the velocity of light in the medium.

Solution:

Given that, the critical angle for TIR, θ_c is 45°.

The Refractive index of the air medium is 1.

Then the refractive index of the medium is given by, 

n = 1/sin 45°

= 1.414

Now, the formula to calculate the speed of light in the medium, v = Speed of light/n

v = 3 × 10⁸ / 1.414

= 2.12 × 10⁸ m/s

Example 2: The glass with the refractive index n₁ = 1.33 is made up of an optical fibre and is surrounded by another glass with the refractive index n₂. Determine the cladding’s refractive index n₂ so that the critical angle between the two claddings is 30°.

Solution:

Given:

Critical angle, θ = 50°

Refractive index, n₁ = 1.33

Critical Angle

θ_c = sin⁻¹(n₂ ⁄ n₁)

n₂ = n₁ sinθ_c

= 1.33 × sin 30°

= 0.665

Example 3: Determine the refractive index of a medium with a critical angle of 45°.

Solution:

Critical angle, θ_c = 45°

Refractive index of the medium, μ = 1 ⁄ sin θ_c

μ = 1 ⁄ sin 45°

= 1.414

Hence, the refractive index of a medium is 1.414.

Example 4: When the wavelengths of light in two liquids, x and y are 250 nm and 500 nm respectively, what will be the critical angle of x relative to y?

Answer:

Given:

Wavelengths, λ_x = 250 nm and λ_y = 500 nm

θ_c = sin⁻¹(n_y ⁄ n_x) = sin⁻¹(λ_x ⁄ λ_y)

θ_c = sin⁻¹(250 nm ⁄ 500 nm)

= 30°

Hence, the critical angle of x relative to y is 30°.

In Physics, total internal reflection is the complete reflection of a light ray within the medium (air, water glass, etc). For example, the total internal reflection of rays of light takes place in a Diamond. Since Dimond has multiple reflecting surfaces through which the Total internal reflection takes place. The total internal reflection occurs when light travels from a denser medium to a less dense medium and the angle of incidence must be greater than the critical angle. The phenomenon of total internal reflection has a wide application in optical devices such as telescopes, binoculars, periscopes, etc. Read more about the concepts of Total Internal Reflection like Total Internal Reflection of Light, definition, critical angle, and total internal reflection, examples, and FAQs, here in this article!