Please make it as clear as possible White light is incident

Please make it as clear as possible.

White light is incident onto a 30 degree prism at a 30 degree angle shown in Fig. 1. Violet light emerges perpendicular to the rear face of the prism. The index of refraction of violet light in this glass is 3% larger than the index of retraction of red light. a) At what angle does red light emerge from the rear face? b) If the beam of white light is dispersed by this prism, how wide is the rainbow spectrum on a screen 2 m away?

Solution

Index for violet is v=sin(30°)/sin(30°);

and v =r*1.03, where index for red is r=sin(30)/sin(x), hence

x=asin(sin(30)/r) = asin(sin(30)*1.03/v) is angle of red on entering the prism prism;

on the other hand when the red is out of prism again

r=sin(y)/sin(x-30°), where y is exit angle of red wrt to horizontal;

v/1.03 = sin(y)/sin(x-30°),

hence y=asin(sin(x-30°)*v/1.03)

=asin(sin(asin(sin30 *1.03/v) -30)*v/1.03)

=asin(sin(asin(1.03*sin30) -30)*(sin30/sin30)/1.03)

= 0.9684°;