The Physics
Hypertextbook
Opus in profectus

# Spherical Lenses

## Problems

### practice

1. Write something.
2. Write something else.
3. Write something different.
4. Write something completely different.

### conceptual

1. ray-diagrams.pdf
The diagrams page 3 of on the accompanying pdf show a pencil placed at five different locations in front of a converging lens. Using a ruler (or other straight edge) and the ray tracing methods described in this section, locate and draw the image of the pencil. For each object position, answer the following questions about the image.
1. Where is the image in relation to the special points on the principal axis? (location)
2. Is the image magnified or reduced? (size)
3. Is the image upright or inverted? (orientation)
4. Is the image real or virtual? (type)
2. ray-diagrams.pdf
The diagrams on on page 4 of the accompanying pdf show a pencil placed at five different locations in front of a diverging lens. Using a ruler (or other straight edge) and the ray tracing methods described in this section, locate and draw the image of the pencil. For each object position, answer the following questions about the image.
1. Where is the image in relation to the special points on the principal axis? (location)
2. Is the image magnified or reduced? (size)
3. Is the image upright or inverted? (orientation)
4. Is the image real or virtual? (type)
3. What kind of eyeglasses can be used to start a fire: those that correct nearsightedness or those that correct farsightedness?

### numerical

1. A typical human eye is 24 mm in diameter can focus on objects that are as close as 15 cm and as far away as the Andromeda Galaxy.
1. What type of lens is found in the eye (converging or diverging)?
2. Is the image produced by the eye…
1. real or virtual?
2. upright or inverted?
3. magnified or reduced?
3. What range of focal lengths can the eye have?
2. A single frame of movie film is 22×12 mm. A projector with a 40 mm lens is used to project an image that is 11×6 m.
1. What kind of lens was used (converging or diverging)?
2. Should the film pass through the projector right side up or upside down?
3. What is the magnification of the projector?
4. How far is the film from the lens?
5. How far is the screen from the lens?
3. You are given two lenses and told to use each one to produce a half size image.
1. The first lens has a focal length of +22 mm. Determine…
1. the type of lens (converging or diverging)
2. the type of image (real or virtual)
3. the object distance
2. The second lens has a focal length of −22 mm.
1. the type of lens (converging or diverging)
2. the type of image (real or virtual)
3. the object distance

### algebraic

1. Prove that image distance equals (M + 1) focal lengths for a converging lens, where M is the magnification.

### statistical

1. thin-lens.txt
A group of physics students placed a candle in front of a thin, converging lens. They placed an index card on the opposite side of the lens and shifted its location until a clear image formed.
1. Transform this data so that a linear fit can be applied.
2. What is the expected value of the slope? Is your calculated value "close enough" to this value?
3. Determine the focal length of this lens?