Set 56 Problem number 23

Problem

A light ray travels through a material whose index of refraction is 1.13 and into a material whose index of refraction is 1.92.  The angle of incidence is 47 degrees.   What is the angle of refraction?

Solution

We call the angle made by the incoming ray and the perpendicular to the interface between the materials the angle of incidence, and the angle made with this perpendicular by the transmitted ray the angle of refraction.

Snell's Law tells us that the ratio of the sines of these angles is inversely proportional to the ratio of the indices of refraction:

• sin(`thetaRef) / sin(`thetaIn) = n1 / n2,

where n1 is the index of refraction in the first material (where the ray comes from) and n2 the index in the second (where the ray is transmitted).

To find the angle of refraction we solve Snell's Law for `thetaRef:

• sin(`thetaRef) = sin(`thetaIn) * n1 / n2, so
• `thetaRef = arcsin [ sin(`thetaIn) * n1 / n2 ].

Thus

• `thetaRef = arcsin[ sin( 47 deg) * 1.13 / 1.92 ] = 25.49 degrees.