Question

A beam of light shines on an equilateral glass prism at an angle of 45∘ to one face (figure (a) below). 1) What is the angle at which the light emerges from the opposite face given that nglass = 1.57? (Express your answer to three significant figures.)

2) Now consider what happens when dispersion is involved (figure (b)). Assume the incident ray of light spans the spectrum of visible light between 400 nm and 700 nm (violet to red, respectively). The index of refraction for violet light in the glass prism is 1.572, and it is 1.568 for red light in the glass prism. Find the distance along the right face of the prism between the points where the red light and violet light emerge back into air. Assume the prism is 10.0 cm on a side and the incident ray hits the midpoint of the left face. (Express your answer to two significant figures.)

Answer 1

Solution:

1)

Given the angle of the prism and incident angle .

From the figure,

On refraction at P,

  

Now, i,e,

On refraction at Q,

  

The angle of emergence is .

2) The light is incident at the midpoint the left face.

  

(a) For violet light

On Refraction at P,

  

Now,

In ,

Now, Using   Law of sines for

  

(b) For red light

On refraction at P,

   

  

Now,

In ,

Now, Using   Law of sines for

  

So, the difference between the points where the red light and violet light emerge from the prism is