Question

5. White light is incident onto a 30 degree prism at an angle of 40 degrees. as shown in the image attached. If the index of refraction through the glass is 2.0 % larger for violet light than red light, what is the angle theta that separates them?

Answer 1

according to your pic index for violet is v=sin(50°)/sin(30°);
and v =r*1.02, where index for red is r=sin(50)/sin(x), hence
x=asin(sin(50)/r) = asin(sin(50)*1.02/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;
? r=r; v/1.02 = sin(y)/sin(x-30°), hence y=asin(sin(x-30°)*v/1.02) =
=asin(sin(asin(sin50 *1.02/v) -30)*v/1.02) =
=asin(sin(asin(1.02*sin30) -30)*(sin50/sin30)/1.02) = 0.997°;