1994 B5

A point source S of monochromatic light is located on the bottom of a swimming pool filled with water to a depth of 1.0 meter, as shown above. The index of refraction of water is 1.33 for this light. Point P is located on the surface of the water directly above the light source. A person floats motionless on a raft so that the surface of the water is undisturbed.

(a) Determine the velocity of the source's light in water.

(b) On the diagram above, draw the approximate path of a ray of light from the source S to the eye of the person. It is not necessary to calculate any angles.

(c) Determine the critical angle for the air-water interface.

Suppose that a converging lens with focal length 30 centimeters in water is placed 20 centimeters above the light source, as shown in the diagram above. An image of the light source is formed by the lens.

(d) Calculate the position of the image with respect to the bottom of the pool.

(e) If, instead, the pool were filled with a material with a different index of refraction, describe the effect, if any, on the image and its position in each of the following cases.

i. The index of refraction of the material is equal to that of the lens.

ii. The index of refraction of the material is greater than that of water but less than that of the lens.