Critical Angle

1. Fill the aquarium with water.
2. Hold your laser or flashlight up to the side of the aquarium so the light is shining into the water.
3. Add the milk one drop at a time, stirring after each drop, until you can see the light beam passing through the water. If you use powdered milk, add a pinch at a time.

Direct the light beam upward through the water so that it hits the surface of the water from underneath. You can shine the beam into the water through the transparent bottom of the aquarium, or in through a side wall. (With the Mini Maglite, you can seal the light in a watertight plastic bag and place the light right in the water!) The beam will be more visible if you can dim the room lights.

Point the beam so that it hits the surface of the water at just about a right angle. In the aquarium, you may be able to see both the reflected beam, which bounces back into the water, and the refracted beam, which comes out of the water and into the air. (Dust in the air helps you see the refracted beam. You can add chalk dust to the air. You can also search for the beam and track it with a piece of paper.)

Notice that most of the beam leaves the water and only a faint beam is reflected back down into the water (click to enlarge the illustration below).

Slowly change the angle at which the beam of light hits the surface of the water.

Notice that the beam reflected into the water grows brighter as the beam transmitted into the air becomes dimmer. Also notice that the transmitted beam is bent, or refracted.

Experiment until you find the angle at which the transmitted beam completely disappears. At this angle, called the critical angle, all the light is reflected back into the water.

In general, when a beam of light (the incident beam) hits the interface between two transparent materials, such as air and water, part of the beam is reflected and part of it continues through the interface and on into the other material. The light beam is bent, or refracted, as it passes from one material into the next (click to enlarge the diagrams below).

The farther the beam is from perpendicular when it hits the surface, the more strongly it is bent. If the light is moving from a material with a low speed of light into a material with a higher speed of light (for example, from water into air), the bending is toward the surface. At some angle, the bending will be so strong that the refracted beam will be directed right along the surface; that is, none of it will get out into the air.

Beyond that angle (the critical angle), all the light is reflected back into the water, so the reflected beam is as bright as the incident beam. This phenomenon is called total internal reflection, because very nearly 100 percent of the beam is reflected, which is better than the very best mirror surfaces.

The critical angle for water is measured between the beam and a line perpendicular to the surface, and is 49 degrees.

Total internal reflection helps transmit telecommunications data along optical fibers. Any light that is not aligned parallel to the axis of the fiber hits the wall of the fiber and is reflected (totally!) back inward, since the angle of incidence with which the light hits the wall is much larger than the critical angle (click to enlarge the diagram below).

This helps prevent the signal from weakening too rapidly over long distances, or from leaking out when the fiber goes around a curve. This demonstration can also be done by replacing the aquarium and water with a small transparent plastic block, which can be bought at a local plastics supply store.