Requires: Transparent cylindrical container (e.g., a drinking glass or a jelly jar with smooth, non-tapering sides, a beaker that doesn't taper; the greater the diameter of the container the more accurate will be the measurements), a candle, a thin ruler or tape measure, water, another liquid such as mineral oil or reasonably clear vegetable oil.

1. Fill a cylindrical transparent container (e.g., a beaker that doesn't taper) with water. Place the beaker on a table with a piece of paper under it and extending out several centimeters.

2. Light a candle and place it as far away from the beaker as possible, and higher than the table or countertop so that light from the candle makes an angle of approximately 5-10 degrees with horizontal as it passes through the beaker. The precise angle is not critical. Darken the room; you may light a second candle or have a little light from another source so you can see your way around. Observe the distinct triangle formed on the tabletop by the light from the first candle passing through the cylinder.

3. Measure the horizontal and vertical distance from the center of the cylinder to the first candle. You will use these distances to determine the angle with horizontal made by the light passing through the cylinder.

4. Measure the dimensions of the triangle and the cylinder, especially making sure you note sufficient information to allow you to determine the radius of the cylinder and how far the apex of the triangle is from the central axis of the cylinder.

5. Now lower the first candle to the height of the cylinder, keeping it as far away as possible from the cylinder. Place a thin ruler underneath the container and extending several cm out from one end. Set the jewel case of a CD or a similar object on its narrow edge on the table so that the square face of the case is vertical. You don't necessarily have to use a CD case; the idea is simply to have an easily moved vertical screen on which to focus light. You might wish to tape white paper to the 'screen' in order to provide a surface on which you can clearly see the focus of the light.

6. Move your screen behind the cylinder so that the light passing through the cylinder will strikes a screen. Move the screen closer to or further from the cylinder and note how a bright vertical region on the screen gets wider or narrower as the screen moves. Note the one position at which the bright region comes into clear focus, forming a thin vertical line. Obtain the data you need to determine the distance of this position from the central axis of the cylinder (again this is easiest if the cylinder is sitting on top of a thin ruler).

7. If the screen is placed as close as possible behind the cylinder, actually touching the cylinder along a vertical line through the center of the bright region, what is the width of the bright region?

8. As the screen is moved from this position to the position of focus, what happens to the width of the bright region? Does the width of the region change linearly with the position of the screen? Should it?

9. As the screen moves away from the cylinder, as it moves past the point of focus, what happens to the width of the bright region?

10. How would you describe the region of space through which the bright light travels after it leaves the cylinder?

11. See the analysis in Class Notes #17. According to this analysis, what is the index of refraction of water?

12. Repeat the second part of this experiment, in which the candle was at the same height as the cylinder, with mineral oil or reasonably clear vegetable oil in place of the water. What is the index of refraction?

13. Repeat the second part of the experiment (again with light passing horizontally through the cylinder) with a stack of CDs. You can use the CDs you obtained for the course or any other stack of CDs. They form a cylinder, perhaps not very high but that doesn't matter. If the light passes horizontally through the CDs it will be focused in the same manner as the light passing through the water or the mineral oil. Determine the index of refraction of the CD material.

14. Return to the bright triangle you observed in the first part of the experiment behind the first cylinder. How can you explain its triangular shape? How would you describe the region of space through which the light forming the triangle travels?

Requires: Thin convex lens (eyeglasses can work--see note at end of #1), candle, measuring device (e.g., tape measure, meter stick).

1. Place a thin convex lens with a focal distance of less than 10 cm at a fixed position so that the lens it is close to vertical and at the same height as the flame of a candle. Place your screen behind the lens and the candle in front of the lens. Darken the room enough that you can observe the focused image of the candle flame on the screen. [NOTE: This experiment can also be performed with a pair of eyeglasses, if you have enough room. The focal length of a pair of eyeglasses, in meters, is the reciprocal of the 'power' of the lens (which is given in diopters). For example a 2.00 lens has a focal length of 1 / 2 meter or 50 cm. A 2.50 lens has focal length 1/2.5 m = .4 m or 40 cm. The distance of the candle would have to be greater than the focal length, so the 10 cm, 20 cm, ..., 50 cm distances would have to be scaled up, with the minimum distance equal to about 1.5 or 2 times the focal length, and distances going up to about 5 times the focal length. You would need a distance equal to the focal length behind the lens in order to form the images.)

2. Place the candle 10 cm from the lens and measure the distance behind the lens at which the image of the candle focuses sharply.

3. Repeat with a candle at distances of 20 cm, 30 cm, 40 cm and 50 cm. Observe how the size of the image changes as the candle is moved further away.

4. Finally repeat with the candle as far from the lens as possible.

5. If i stands for the distance of the focused image on the screen behind the lens and o for the distance of the object, in this case the candle flame, which is being focused, determine the value of the quantity 1 / i + 1 / o for each of your measurements.

6. Determine how close you can get the candle flame to the lens and still form a clearly focused image on the screen.

7. Explain everything you have observed in terms of a ray diagram.

8. Now hold a thin convex lens directly above a printed page. Start with the lens in contact with the page and slowly bring it back toward your eye. What happens to the image you see? Explain what you see in terms of a ray diagram.