The Refraction of White Light in a Prism: Dispersion

 

Triangular prisms can be used to separate white light in its spectral components (colours).  This occurs because the angle of refraction depends on the index of refraction, which is unique for each wavelength.

 

Recall that in the expanded form of Snell's Law, the wavelength and index of refraction are related to one another as follows:

 

 

When any light wave enters the prism from the air, its wavelength is compressed as it slows down.  Because the refractive index of air ( n 1 ) is equal to 1.0, the ratio of the wavelength before and after the refraction determines the refractive index of the medium for each wavelength.


Given that white light is made up of many different wavelengths, or colours, each one will refract at a slightly different angle causing them to emerge at different points, effectively separating the colours and producing a spectrum.  To illustrate and explore this process, a ray diagram and some basic triangle mathematics are required.

 

Recall the basic properties of all triangles:

  • The sum of the interior angles in a triangle is 180°.  According to the noted triangle, a + b + c = 180°.
  • The complimentary angles are angles that add to form a 90° angle or right angle.
  • The supplementary angles are angles that add to form a 180° angle or a straight angle.

Try This
Using the basic properties of all triangles, solve the three questions below.

1.  In the diagram on the left, the blue dashed lines represent surface normals to the triangle.  These lines form 90° angles with the respective faces they pass through.  Explain how you know that angle a = 70°.

 

2.  Determine angle b if angle a is 70°.

 

3.  Knowing angle b, determine angle c.

 

 

Simulation: Tracing a Ray Through a Prism

The Refraction simulation below can be used to verify ray diagrams and calculations that demonstrate that different colours of light separate (disperse) as they pass through a prism.   Follow the simulation instructions below and note that each prism in the simulation is an equilateral prism with 60° angles at each corner.

 

Open the  Refraction  simulation and select "Prism Break". Drag a triangle prism into the path of the laser, set the refractive index of the prism to glass (n=1.50), select "white light" from the menu on the right, and rotate the prism (by using the brown handle on the right corner) to an angle of 100° as shown in the diagram on the right.  This will make the incident angle for the ray entering the prism  θ in  = 43.68°.

  1. Using Snell's Law and the refractive index of air ( n  = 1.00), show the calculations for determining angle a.  
  1. Using the techniques developed in recent Try This activities and the fact that the prism is an equilateral triangle, calculate the angles b, c, d, and  θ out .  
Performing the mathematical analysis for two rays with different wavelengths (and indexes of refraction) will demonstrate the process of dispersion in a prism.

 


Read
Read "Prisms-Dispersion of White Light" on pages 675-676 of your textbook for more information on the composition of white light.