You can determine the index of refraction of a substance by determining its critical angle. (a) What is the index of refraction of a substance that has a critical angle of 47.3° when submerged in ethanol, which has an index of refraction of 1.361? (b) What would the critical angle be for this substance in air?

a) 1.851

b) 32.68°

Explanation:

The relation between critical angle and index of refraction is as follows

Sin C = 1 / μ

C is critical angle and μ is refractive index.

Given C = 47.3

Sin 47.3 = 1 / μ

0.735 = 1 / μ

μ = 1 /.735

= 1.36

This is with respect to ethanol.

1.36 = refractive index of material / refractive index of ethanol

refractive index of material = 1.36 x refractive index of ethanol

= 1.36 x 1.361 = 1.851

If critical angle for this substance be A

Sin A = 1 / 1.851 =.54

A = 32.68°.