Question

Now consider θc, the angle at which the blue refracted ray hits the bottom surface of the diamond. If θc is larger than the critical angle θcrit, the light will not be refracted out into the air, but instead it will be totally internally reflected back into the diamond. Find θcrit.

Answer 1

θ_c = 24.4º

Step-by-step explanation:

To find the critical angle, let's use the law of refraction where index 1 refers to the incident medium (diamond) and index 2 refers to the medium where it is to be refracted (air)

n₁ sin θ₁ = n₂ sin θ₂

for the critical angle the ray comes out refracted parallel to the surface, therefore the angle is

θ₂ = 90

n₁ sin θ₁ = n₂

θ_c = θ₁ = sin⁻¹
`(n_2)/(n_1)`

the index of refraction of the diamond is tabulated

n₁ = 2.419

let's calculate

θ_c = sin⁻¹ (
`(1)/(2.419)`)

θ_c = 24.4º