Interactive Lecture Demonstration 12 – Prisms

In this demonstration, we will predict and then observe the paths of light beams sent through prisms of various shapes. All of these experiments rely on Snell's Law, which relates the angle of incidence q_i to the angle of refraction q_r when light passes from one medium into another:

n_i sinq_i = n_r sinq_r ,

where n_i and n_r are the indices of refraction in the incident and refracting media. Throughout this activity, we will use light that has passed through a narrow slit after leaving the light source, forming a thin ray of light. We will represent those rays by directed lines in our diagrams.

1. Suppose a light ray is sent towards a rectangular prism. If the light is incident at a normal (i.e. 90 degree) angle to the surface of the prism, predict what will happen to the beam when it a) enters the prism and b) leaves the prism. Sketch your predicted path of the light ray on the diagram below. Then observe what actually happens.

2. The angles of incidence and refraction are always measured from the normal to the boundary of two media. Since the angle of incidence in the first example was 0 degrees, Snell's Law predicts that the angle of refraction should also be 0 degrees, i.e. there is no refraction of the light ray in that situation. Suppose we tilt the rectangular prism now, so that the light ray will hit the prism at a non-zero angle of incidence. Predict what will happen to the light ray when it enters the prism, then when it exits the other side of the prism. Sketch your predicted path of the light ray on the diagram below. Then observe what actually happens.

3. The light ray was refracted twice in the last experiment. When light travels from a medium of low index of refraction into a medium of higher index of refraction (for example, from air into plastic), the light is bent towards the normal to the boundary of the media. In traveling from a medium of higher index of refraction into one of lower index of refraction (from plastic into air, in this case), light is bent away from the normal. In the situation of #2, since the sides of the rectangular prism are parallel to each other, the angle of refraction of the incoming light ray (at the air/plastic interface) is equal to the angle of incidence of the refracted ray (at the plastic/air interface). Thus, Snell's Law predicts that the angle of refraction at the second interface must be equal to the angle of incidence at the first interface. In other words, the light ray exits the prism moving parallel to the direction it had before it entered the prism.

We can use the results of situation #2 to determine the index of refraction of the plastic prism. Measure the angles of incidence and refraction, then use Snell's Law to calculate n for the plastic.

4. Now we will use a triangular shaped prism. The base of the triangle will be parallel to the direction of the incoming light ray. Predict what will happen to the ray by the time it leaves the prism – will it be bent towards the base, away from the base, or leave the prism in a direction parallel to the direction of the incoming ray ? Sketch your predicted path of the light ray below.

5. Observe the actual path of the light ray. You may notice that the white light has been spread into a spectrum of colors. Which color deviates most from the direction of the initial ray ? Which color deviates least ? What can you infer from these observations about the index of refraction of the plastic ?
6. Do you think the angle through which the initial light ray is bent by the triangular prism depends on the prism's angles ? If so, what shape prism should be used to bend the initial light ray through a greater angle ?

7. Could a triangular prism be used to focus several rays of light to a single point beyond the prism ?

8. Now consider the arrangement of two prisms shown below. This arrangement will focus the two beams of light labeled A and B to a single point P beyond the prisms. Will the prisms also focus beams C and D to the same point P ? If not, can you think of another arrangement of prisms that would focus all four rays to the same point P ?

9. Now we will return to a single triangular prism. If we rotate the prism so that the light ray hits the plastic/air interface at a large enough angle (called the "critical angle"), the light will be refracted so that it exits the prism moving parallel to the surface of the prism (i.e. it does not really exit the prism at all). In that situation, the angle of refraction is 90 degrees. If we further rotate the prism so that  the light hits the plastic/air interface at an even greater angle, no light will pass through the prism surface. This is the phenomenon of total internal reflection. Use the index of refraction you determined in #3 to predict the critical angle for this situation. Then do the experiment and measure the actual critical angle.