Question

A light beam containing red and violet wavelengths is incident on a slab of quartz at an angle of incidence of 47.5

Answer 1

Use Snell's Law. If n1 is the index of refraction of air, x1 be the angle of incidence, n2 be the index of refraction of the quartz and x2 the angle of regraction, then
n1sin(x1) = n2sin(x2).

Since n1 = 1 and x1 = 47.5 degrees, we have

sin(47.5) = n2sin(x2), or x2 = sin^-1(sin(47.5)/n2).

For red light, this is sin^-1(sin47.5/1.455) = 30.44 degrees
For blue light, this is sin^-1(sin47.5/1.468) = 30.139degrees.

So the disperson is 30.44-30.139 = 0.301 degrees.