Question

Two monochromatic light sources produced green and orange lights. The two lights in water strikes a diamond surface at the same point of incidence and at an angle of 52.0° with the surface (not the normal). The indices of refraction of diamond for green and orange lights are 2.45 and 2.42 respectively. (a) Calculate the angle of dispersion of the two colors in diamond if the lights are passing from a liquid to diamond (index of refraction of water is 1.33). (b) Sketch and label clearly the path of the lights on the figure below. Show all the necessary angles and labels.

Answer 1

from the given data,

angle of incidence, theta_i = 90 - 52 (since we always measure angle of incidence between normal to the surface and incident ray)

= 38 degrees

n_green = 2.45
n_orange = 2.42

n_water = 1.33

let theta_green is the angle of refraction for green color
ans theta_orange is the angle of refarction for orange color.

Use Snell's law for green light

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

sin(38)/sin(theta_green) = n_green/n_water

sin(theta_green) = sin(38)*n_water/n_green

= sin(38)*1.33/2.45

= 0.334216

theta_green = sin^-1(0.334216)

= 19.52 degrees

Use Snell's law for orange light

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

sin(38)/sin(theta_orange) = n_orange/n_water

sin(theta_orange) = sin(38)*n_water/n_orange

= sin(38)*1.33/2.42

= 0.338359

theta_orange = sin^-1(0.338359)

= 19.78degrees

angle of dispresion of the two colors = 19.78 - 19.52 = 0.26 degrees

b)