Physics 103

Reflection and Refraction


Reflection and refraction are familiar optical phenomena. The reflection of light from smooth polished surfaces, such as mirrors or surfaces of water, enables us to view (virtual) images of ourselves and other objects. The refraction of light at an interface makes a stick in a pond, or a spoon in a glass of water, appear to bend. Painters of the Renaissance worked hard to represent these phenomena accurately, and they are of interest in modern computer graphics. Complex optical systems are made of individual components, mirrors, lenses, crystals, and prisms which control the reflection and refraction of light

These phenomena can be modeled by the behavior of "light rays," straight lines imagined to obey the simple rules of "ray tracing." When a light ray encounters a boundary between two different media, some of the light is reflected from the boundary while some passes into the material on the other side of the boundary. The angles at which the light rays travel are determined by the laws of reflection and refraction:

1. The angle of reflection equals the angle of incidence

2. The angles of incidence and refraction are related through Snell's law

where n1 is the index of refraction of the incident medium and n2 is the index of refraction of the transmitting medium.

3. The incident ray, the reflected ray, and the normal all lie in the same plane.

Note that the angles of incidence, reflection, and refraction are always measured with respect to the normal of the boundary between the two media.



The experimental setup is illustrated below. A ray of light is incident from air (medium #1) into a semicircular chunk of plexiglas (medium #2). The light source (symbolized by a red dot in the applet) can be dragged with the mouse to change the angle of incidence. The angles referred to in the laws of reflection and refraction are indicated with black arcs (notice these angles are measured from the normal to the interface). We will look at the behavior of the rays at the plane interface (the straight side of the plexiglas).

First let the light be incident from below. The light at the plane interface is traveling from a less dense medium (air) into a more dense medium (Plexiglas). Does Snell's law predict that the refracted ray will be bent towards or away from the normal?

Second, drag the light source around to the top, so that the light strikes the plane interface from above. Now the light at the plane interface is traveling from a more dense medium (medium #1, Plexiglas) into a less dense medium (medium #2, air). In this case one can see a phenomenon called "total internal reflection." Verify from Snell's Law that no transmitted ray is possible if the incident angle is larger than a critical value given by

We have indicated a peculiar horizontal ray skimming the interface in this case! This is to remind us that there is actually a surface wave, sometimes called an "evanescent wave," in total internal reflection. Strictly speaking, geometrical optics is not able to describe this aspect of the light's behavior.