1. The index of refraction of air decreases with increasing temperature. (a) A mirage is formed when the air gets gradually cooler with increasing altitude. Make a sketch of the actual and apparent paths of a ray traveling from the an object towards an observer and show why the eye sees the mirage. (b)What might happen if the air grew gradually warmer with altitude? This often happens over bodies of water or snow-covered ground; the effect is called looming. Make a sketch as in part (a).
2. Determine the minimum height of a wall mirror that will permit a 6-ft person to view his/her entire height. Sketch rays from the top and bottom of the person, and determine the proper placement of the mirror such that the full image is seen, regardless of the person's distance from the mirror.
3. A small source of light at the bottom face of a rectangular glass slab 2.25cm thick is viewed from above. Rays of light exit the top surface in a circle of 7.60 cm in diameter. Determine the refractive index of the glass.
4. Fill in the following table. Each row refers to a combination of an object and either a plane mirror, a spherical concave mirror, or a spherical convex mirror. Distances are in cm. If a number lacks a sign, find the sign. Sketch a ray diagram for each combination, showing enough rays to locate the image.
| Type | f | R | si | so | m | Real? | Inverted? |
|---|---|---|---|---|---|---|---|
| a. Concave | 20 | +10 | |||||
| b. | +10 | +1.0 | No | ||||
| c. | +20 | +30 | |||||
| d. | +60 | -0.5 | |||||
| e. | +40 | -10 | |||||
| f. | 20 | +0.1 | |||||
| g. Convex | 40 | 4.0 | |||||
| h. | +24 | 0.5 | Yes |
5. Fill in the following table. Each row refers to a combination of an object and a converging (C) or diverging (D) thin lens. You may not be able to determine every number in the table. Distances are in cm. If a number lacks a sign, find the sign (except for the index of refraction). Sketch a ray diagram for each combination, showing enough rays to locate the image.
| Type | f | R1 | R2 | so | si | n | m | Real? | Inverted? |
|---|---|---|---|---|---|---|---|---|---|
| a. C | 10 | +20 | |||||||
| b. | +10 | +5.0 | |||||||
| c. | 10 | +5.0 | >1.0 (find #) | ||||||
| d. | 10 | +5.0 | < 1.0 (find #) | ||||||
| e. | +30 | -30 | +10 | 1.5 | |||||
| f. | -30 | +30 | +10 | 1.5 | |||||
| g. | -30 | -60 | +10 | 1.5 | |||||
| h. | +10 | 0.50 | No | ||||||
| i. | +10 | -0.50 |
6. The disk of the Sun subtends an angle of 0.533 degree at the Earth. What are the position and diameter of the solar image formed by a concave spherical mirror with a radius of curvature of 3.00m?
Problems extracted from Haliday, Resnick, & Walker, Serway & Beichner, Pedrotti & Pedrotti
Last updated February 23, 2005