Week 30 (Mar. 18 - 22)

Reading: The nature of light and the laws of geometric optics (Chap. 35)

Key Topics:
the speed of light, ray approximation, reflection, refraction, dispersion, total internal reflection, prisms and rainbows

Lab: geometric optics laboratory. Due Wed. March 27.

1. Tape a large piece of white paper to a flat piece of cardboard or cork board. Using supports, stand up two flat mirrors in the center of the cork board.
2. Begin with the mirrors in a straight line. Use a pencil to trace the location of the mirrors on the paper. Now insert a stick pin into the cardboard a few centimeters in front of the silvered face of the mirrors. Look at the image of the pin formed in the mirrors. Now attempt to place a second stick pin behind the mirrors so that its location is exactly where the image of the first pin appears. Take a photo of your setup for your lab book. Now use a small ruler to measure the distance between the pin in front of the mirror and the pin behind the mirror. Are the object (the first pint) and the image (the second pin) equidistant from the mirror? Next, draw an eye on the paper behind the pin but a bit off to one side of the pin. This represents a position from which the image can be observed. Then use a straight-edge to trace the path of a ray of light that travels from the stick pin, bounces from the mirror, and finally arrives at the position of the observing eye. Remember that the ray must obey the law of reflection! Before going on, be sure to write down your procedure and results in your laboratory notebook. Your lab notebook should include your ray-tracing diagram.
3. Repeat this experiment, but now with the mirrors separated by 90 degrees (they are arranged at a right angle). Trace the mirrors on the paper. Put the pin a few cm from the joint and equidistant from the mirror faces. How many images do you now see? Once again, insert pins at the locations of the images, to the best of your ability. Do you notice a symmetrical arrangement of the images? Again, draw an eye behind the pin, and trace the rays of light coming from the object, bouncing from the mirror, and arriving at the eye. Be sure that the ray always obeys the law of reflection when it bounces from a mirror! Record your results and your ray-tracing diagram in your laboratory notebook.
4. Repeat the experiment with the mirrors separated by 60 degrees and, if possible, 45 degrees. For each of these, record your results and your ray-tracing diagram in your laboratory notebook.

Homework Problems: Due Monday March 25.

1. Ray bouncing from V-mirrors: Suppose that two flat mirrors are stood up on a table top in a v-configuration so that there is a 60 degree angle between their mirrored surfaces, which face one another. A ray of light is fired across the table toward the mirrors. It enters the region between the mirrors so that there is a 30 degree angle between the ray and each of the mirrors' surfaces.
• If the ray does not strike at the vertex (junction) of the mirrors, then how many times will the ray bounce from the mirrors before escaping? Make a ray diagram to illustrate how you solved this problem geometrically.
• What if the beam makes an angle of 15 deg ( instead of 30 degrees) with one of the surfaces?
2. Hanging mirror: A man stands 100 cm in front of a mirror that is 50 cm high. He holds a two-meter long tape-measure against his body so that the top of the tape measure is at the level of his eyes and the two-meter mark on the tape measure is at the level of his feet. The mirror is hanging on the wall so that the top of the mirror is level with his eyes.
• Can the man see the entire length of the tape measure? If not, then what portion of the tape measure can he see when he looks in the mirror? Draw a picture with a ray diagram to illustrate how you solved this problem using geometry.
• What if the mirror is now tipped away from the wall so that the top of the mirror is 95 cm away from his eyes and the bottom is still 100 cm away from him? Which portion of the tape measure can the man now see? Draw a picture with a ray diagram to illustrate how you solved this problem using geometry.
• If the mirror was curved (convex), could he see more or less of the tape measure? What about if it was concave?
General College Physics