This is a perfect way to see for yourself how light moves when it encounters mirrors and lenses.
What You Need
- laser pointer
- set of lenses, including convex, concave, rectangular, and semicircular lens; rectangular prism and 60 and right-angle prisms (90°, 45°, 45°) and (90°, 30°, and 60°)
- 2 small flat mirrors
- sheet of paper (plain or gridded)
- dark room
- Caution—You should use a low-power laser pointer and be careful not to shine the laser where it could hit anyone's eyes. Remember, you are working with optical devices that change the path of the light, so be careful to avoid stray light rays that could affect anyone's eyes.
- Place your object lens (or mirror) on a flat table.
- Place a sheet of paper underneath the lens.
- Trace the outline of the lens on your paper. Leave enough room to draw incoming and outgoing lines.
- Darken the room.
- Shine the laser at a slight angle, so its straight line path can be seen on the paper.
- For each of the lenses, put three or more dots along the path to define the incident path.
- Observe its path through the lens (or reflected from the mirrors). You may need to slightly adjust the angle (to the plane of the table) to make the transmitted ray visible. Depending on your lenses, you may not be able to see the laser light going through the lens. Also, be careful not to mistake light that may sneak underneath the lens as a ray that follows the intended optical path through the lens. Also (again depending on your lenses), you may need a slightly different angle to make the incident laser line visible as you would need for the refracted line. If this is the case, make sure you come into the lens along the same incident line that you drew.
- Make three or more dots to define the refracted (or reflected) paths.
- Make a dot where the light enters the lens and where it leaves the lens.
- Connect the dots with straight lines showing the incident (incoming) line, the straight line through the lens (which is the refracted line), and the transmitted or reflected lines.
- Explore as many of the following optical objects as you have available. The following lists several specific things to focus on.
(Note: All this can be done, if you prefer, on a magnetic chalkboard using lenses with magnetic backs. You can either glue strong magnets to your lens or simply hold the lens to the chalkboard. Make sure that the magnetic chalkboard is strong enough to hold the lens securely and that the magnet does not block the path of the light. Laser levels may be useful because they have built-in angles to make the line visible along a surface. However, they may be a little trickier to focus all the way through the lens.)
Draw a perpendicular line to the surface of the mirror. Shine the laser at the point where the perpendicular line meets the mirror. Place dots along the incident line and the reflected line, and then connect the dots. Compare the incident angle with the reflected angle. Try this for several sets of angles (Figure 78-1).
Mirrors at a right angle
Shine the laser on one of the mirrors and trace its path (by placing dots along the path and connecting them). The path should hit the second mirror, and then reflect off the second mirror. Try this for several angles of incidence on the first mirror. (If you like geometry, set the mirrors at an acute angle. Then, predict and test the angle of the outgoing ray for a given angle of incidence.)
A convex lens is the one that is thicker at the middle than at the ends. Draw a centerline perpendicular to the axis of the lens. Trace the following paths: a) a straight line along the center line through the center of the lens, b) a line above the centerline running parallel to the centerline, c) a line below the centerline running parallel to it. Trace all the lines. Notice where the three lines cross. Measure that distance and put a dot on the centerline on the incident side of the lens that same distance from the lens. Direct the laser at any angle through that dot and trace its path through the lens. Try this for several angles.
A concave lens is the one that is thinner at the middle than at the ends. Draw a centerline perpendicular to the axis of the lens. Trace the following paths: a) straight line along the center line through the center of the lens, b) a line above the centerline running parallel to the centerline, c) a line running below the centerline running and running parallel to it. Trace all the lines. How do these results compare with those from the convexlens?
The semicircular lens has one circular side and one flat side. Place the circular side toward you. Trace the lens and draw a centerline on the flat side. Shine the laser at a 30-degree angle to that centerline, but hit the point where the centerline meets the flat side of the lens. This particular arrangement avoids refraction in the glass because the light comes in perpendicular to the tangent at the circular edge. In this case, the only refraction that occurs is at the glass-to-air interface. Observe what happens for different angles. Take it to the extremes of high and low angles of incidence.
Draw a perpendicular line to one of the edges of the prism. (Make sure the edges you are using are clear and not frosted.) Direct the beam toward the point where the perpendicular meets the edge and trace the path of the laser through the prism at various angles.
There are two main types of right-angle prisms: 90°, 45°, 45° and 90°, 30°, 60°. Here is a challenge. Try it either by working out the light rays first or by just playing with the prisms and figuring it out by trial and error:
- How can you direct a light ray through the prism and have a ray emerge at 90 degrees to the incoming ray (based only on total internal reflection)?
- How can you direct a light ray through the prism and have a ray emerge at 180 degrees to the incoming ray heading back in the direction that it came from (also based only on total internal reflection)?
The measurements should validate the idea that the angle of incidence equals the angle of reflection.
Mirrors at a right angle
Regardless of the angle at which the laser ray strikes the mirror, the ray reflected from the second mirror will be parallel to the incoming ray, but heading in the opposite direction.
Rays striking the lens traveling along the centerline will go straight through the lens without being diverted. Rays traveling parallel to the centerline bend toward the centerline and cross at a point (called the focal point) on the opposite side of the lens.
Rays passing through a focal point on the same side of the lens as the laser (same distance as the focal point measured previously) emerge from the lens parallel to the centerline.
No matter where the rays hit the lens, the rays do not cross. Above the centerline, the rays bend up. Below the centerline, the rays bend down.
Rays hitting the semicircular side and directed toward the center of the circle bend (or refract) only when emerging from the glass to the air.
Rays emerging from the lens are parallel to the incident ray, but offset in the direction that rays move through the lens. As with all these observations, the path the ray takes in the prism is a straight line.
Rays striking one of the two shorter edges of the (90°, 45°, 45°) prism make a 90-degree turn, and then reflect back.
Rays striking the longer (hypotenuse) edge of the (90°, 30°, 60°) prism make a 180-degree turn, and then reflect back.
These produce a range of transmitted angles and conditions for total internal reflection.
Why It Works
Lenses are optical devices that refract light passing from one medium (air) through another (glass or plastic), and then typically back to the air. At each interface, the light is bent according to Snell's law.
Mirrors, whether involving one or many surfaces, reflect light in such a way that the angle of incidence equals the angle of refraction.
Other Things to Try
The lenses and mirrors previously described can also be studied using the following additional methods:
- Ray tracing with split beam. You can make or buy an apparatus that projects several parallel beams of light. Basically, the apparatus consists of a bulb covered by an enclosure that shines through parallel openings in the side of the enclosure. The beams of light, when directed at the various lenses and mirrors, show the properties of the devices in a graphic and intuitive way. This approach is better suited to smaller lenses and mirrors.
- Ray tracing by locating images. A more traditional approach is to view a vertical object such as a pin or a nail through the lens. This is accomplished by: a) tracing the outline of the lens, b) locating the position of the image seen through the lens, and c) drawing a line to show the incident, refracted, and transmitted paths of light.
Lenses and mirrors divert light in predicable ways. Lenses are based on refraction, while mirrors employ reflection. Some lenses are converging and direct rays of light passing through them through a focal point. Other lenses are diverging and direct the rays of light in such a way that they never cross. The reflection at the surface of any plane mirror occurs in such a way that the angle of incidence equals the angle of reflection.