Question

Diamond has an index of refraction of 2.419. What is the critical angle for internal reflection inside a diamond that is in liquid of index of refraction n=2? A) 15.4° B) 55.8° C) 26° D) 20° E) 39°

Answer 1

Answer:

B) 55.8°

Explanation:

n₁ = Refractive index of liquid = 2

n₂ = Refractive index of diamond = 2.419

Here it can be seen that the light ray is in the more dense medium and approaching the less dense medium which is a case of total internal reflection.

Critical angle

$\theta_r=sin^{-1}\frac{n_1}{n_2}\\\Rightarrow \theta_r=sin^{-1}\frac{2}{2.419}\\\Rightarrow \theta_r=sin^{-1}0.826\\\Rightarrow \theta_r=55.7701^{\circ}$

∴ Critical angle is 55.8°