Answer to Question #144650 in Optics for Promise Omiponle

Question

You can determine the index of refraction of a substance by measuring its critical angle for total internal reflection.

Randomized Variables
Θc,w = 74.6°

(a) What is the index of refraction of a substance that has a critical angle of 74.6° when submerged in water (with index of refraction 1.333)?
(b) What would the critical angle be for this substance in air?

Answer 1

(a)

$n_1 = ?$

$n_2 = 1.333$

$θ_c = 74.6º$

$n_1 = \frac{n_2}{sin(θ_c)}$

$n_1 = \frac{1.333}{sin(74.6º)} = \frac{1.333}{0.9641} = 1.3826$

(b) $θ_c = sin^{-1}\frac{n_2}{n_1}$

$θ_c = sin^{-1}\frac{1.000293}{1.3826}= sin^{-1}(0.72348) = 46.34º$