Question

A ray of sunlight is passing from diamond into crown glass; the angle of incidence is 36.00°. The indices of refraction for the blue and red components of the ray are: blue (ndiamond = 2.444, ncrown glass = 1.531), and red (ndiamond = 2.410, ncrown glass = 1.520). Determine the angle between the refracted blue and red rays in the crown glass.

Answer 1

for Blue light
theta_i = 36 degrees
n1 = 2.444
n2 = 1.531
let theta_r is the angle of refraction of blue light.

use Snell's law,

sin(theta_i)/sin(theta_r) = n2/n1

sin(36)/sin(theta_r) = 1.531/2.444

==> sin(theta_r) = sin(36)*2.444/1.531

= 0.9383

theta_r = sin^-1(0.9383)

= 69.77 degrees

for red light
theta_i = 36 degrees
n1 = 2.410
n2 = 1.520
let theta_r is the angle of refraction of red light.

use Snell's law,

sin(theta_i)/sin(theta_r) = n2/n1

sin(36)/sin(theta_r) = 1.52/2.41

==> sin(theta_r) = sin(36)*2.41/1.52

= 0.93195

theta_r = sin^-1(0.93195)

= 68.74 degrees

the angle between the refracted blue and red rays in the crown glass = 69.77 - 68.74

= 1.030 degrees <<<<<<<---------Answer