Question

An incident ray strikes a piece of diamond at an angle of 40.5 degrees. The index of refraction of air is 1.0003 and the index of the refraction of diamond is 2.42. What is the angle of refraction?

Answer 1

The angle of refraction is 15.6 deg.

When a ray of light passes from medium 1 to medium 2, the refractive index of medium 2 with respect to 1 is the ratio of the absolute refractive index of medium 2 and medium 1

$_1n_2 =\frac{n_2}{n_1}$

When light passes from air into diamond, with the given values of refractive indices,

$_an_d =\frac{n_d}{n_a} =\frac{2.42}{1.0003} =2.4193$

According to Snell's law,

$_an_d=\frac{sini}{sinr} \\ sinr=\frac{sini}{_an_d} =\frac{sin(40.5)}{2.4193}=0.2684\\ r=arcsin(0.2684)=15.57 deg$

The angle of refraction is 15.6 deg

Answer 2

The correct answer on is 15.6 degrees.