Physics Experiment

Reflection in Multiple Mirrors

Purpose:

To investigate the nature of multiple images in a system of mirrors.

Discussion:

At the barber shop or hairdresser, have you ever used 2 mirrors to look at the back of your head - one mirror in front of you and the other behind? If so (and if you are a careful observer), what you saw may have surprised you. This phenomenon, an extreme number of multiple images in two parallel mirrors, is known to physicists as the "barbershop effect".

Perhaps you have been fascinated by the colorful and symmetric changing images in a kaleidoscope. The kaleidoscope uses multiple images produced by a simple system of plane mirrors. These phenomena can be explained using the Law of Reflection.

Equipment:

2 plane mirrors

mirror support

protractor

pin

paper

tape

Procedure:

Apparatus:

Tape the mirrors together so that they almost touch along one edge and can be adjusted to form an angle between them. One way to do this is to place the mirrors face to face and place a piece of tape around one end of the two mirrors to form a "hinge".

Part 1 Perpendicular Mirrors:

Draw a 90^o angle near the center of a piece of paper, and arrange the mirrors so that their reflecting surfaces (fronts or backs?) are on the lines. The mirrors should be arranged so that there is a precise 90^o angle between them. Place one pin in front of the mirrors (not halfway between them is best) and look at the images of the pin in the mirrors. Look carefully - there are not 2 images!
Using the ray method from your previous experiment, locate all of the images of the pin. Put this sheet of paper aside.

Part 2 Mirrors at other angles:

On a clean sheet of paper, draw a line to represent one mirror surface. Place your mirrors on the sheet so that one mirror lies along this line. Mark the position of the other mirror and the point of intersection with the other mirror.
What you are going to do is count the number of images you can see for angles other than 90^o. In order to do this a physicist would record her data in a data table. A data table was supplied for you in previous experiments, but physicists do not find ready-made data tables in their laboratories, so now it is time to begin constructing your own data table. A sample data table is shown below that you may use as a pattern for your own data table. Notice that the data table contains the name of the experiment, the date the data was taken, and the name(s) of the person(s) who took the data. Also be sure to label each column of the data table and indicate the units in which each number was measured. (For this activity, angles are measured in degrees and there is no unit for the number of images, since they are counted.)
Place a pin in front of the mirrors and count the images you see. Record this information in the data table. It may be difficult to decide how many images you actually see for some angles - do your best here. If you cannot decide whether there are 6 or 7 images, put both numbers in the data table. The precise number of images will not affect your analysis.
Adjust the mirrors to another angle, count the images, and record the data. Continue this procedure for several angles.

Analysis:

Part 1 - Perpendicular Mirrors:

Let's see if you can explain how the 3 images are seen in the perpendicular mirrors using the Law of Reflection. What you can do is trace the path of a light ray from your eye back to the object on your data sheet. Refer to the figure below

Pick a convenient spot on the object side of the mirror to represent the location of your eye. Label this point E for convenience.
If you see an image in a particular direction, light had to arrive at your eye from that direction. Draw a line representing a light ray between one image and point E (your eye). Note where it strikes the mirror.
Now, the light ray you just drew did not actually come through the mirror from the image, it was reflected from the front of the mirror. Draw a normal to the mirror at the point the ray strikes the mirror and measure the angle of reflection. Construct the angle of incidence for the ray on the other side of the normal. Does the light ray pass through the object?
Repeat steps c and d above (do not move point E - your eye) for each image that you find. Be sure that you understand how each image is formed by the mirrors and the Law of Reflection.

Part II - Mirrors at Other Angles.

What happens to the number of images as the angle between the mirrors decreases?
How are these multiple images formed?
How many images would you expect to see if the mirrors are parallel? (Try it!)

References:

Genzer & Younger, Laboratory Investigations in Physics, p. 157-162
Robinson, Conceptual Physics Laboratory Manual, p. 249-50, 253-254

last update October 27, 2007 by JL Stanbrough