Prisms are triangular pieces of glass or plastic. As light enters a prism it is refracted, and then it refracts again when departing. Before we look more closely at prisms, let us examine a piece of glass or plastic which has parallel sides.
In our study under Refraction, we found that the light ray going into an object with parallel sides exits going in the same direction. It will be displaced to one side or the other, but Snell's Law predicts the two angles are equal.
n1 sin q1 = n2 sin q2
n2 sin q3 = n1 sin q4
n1 sin q1 = n2 sin q2 = n2 sin q3 = n1 sin q4
n1 sin q1 = n1 sin q4
q1 = q4
And the same phenomenon occurs whether the medium inside the "box" is more or less dense than the surrounding material.
With non-parallel sides, we don't expect a prism to behave in exactly the same manner. The light going into the prism is refracted closer to the normal, making qP smaller than qA.
The angle formed at the next surface, q'P, is not equal to qP. This means that the next equation, although simply a new application of Snell's Law, does not contain the same size angle as we saw in the case of parallel sides. (It is possible that they would be the same sized angle, but generally not highly likely.)
A prism bends the light two times, having a cumulative effect of bending it away from its original direction. The general direction of bending is towards the wide portion or the base of the prism.
What would happen if the prism were air and the surroundings were more dense?
With a less dense "prism," the initial bending is away from the normal making the angle inside the air larger than the angle outside the air.
The second bending is from a larger angle in air to a smaller angle in the new medium.
The cumulative effect is to double-bend the light towards the narrow part or the apex of the prism.
Future versions of these pages will explore the peculiar effect of prisms which enables them to spread light out into its component colors. For now, rest assured that the behavior of light rays in prisms follows the general rules discussed before.
