Chapter 24

Problem 1

An object is placed $12.0 \mathrm{cm}$ in front of a lens of focal length $5.0 \mathrm{cm} .$ Another lens of focal length $4.0 \mathrm{cm}$ is placed $2.0 \mathrm{cm}$ past the first lens. (a) Where is the final image? Is it real or virtual? (b) What is the overall magnification? (interactive: virtual optics lab).

Problem 2

A converging lens and a diverging lens, separated by a distance of $30.0 \mathrm{cm},$ are used in combination. The converging lens has a focal length of $15.0 \mathrm{cm} .$ The diverging lens is of unknown focal length. An object is placed $20.0 \mathrm{cm}$ in front of the converging lens; the final image is virtual and is formed $12.0 \mathrm{cm}$ before the diverging lens. What is the focal length of the diverging lens?

Problem 3

Two converging lenses are placed $88.0 \mathrm{cm}$ apart. An object is placed $1.100 \mathrm{m}$ to the left of the first lens. which has a focal length of $25.0 \mathrm{cm} .$ The final image is located $15.0 \mathrm{cm}$ to the right of the second lens. (a) What is the focal length of the second lens? (b) What is the total magnification?

Problem 4

A converging lens with a focal length of $15.0 \mathrm{cm}$ and a diverging lens are placed $25.0 \mathrm{cm}$ apart, with the converging lens on the left. A 2.00 -cm-high object is placed $22.0 \mathrm{cm}$ to the left of the converging lens. The final image is $34.0 \mathrm{cm}$ to the left of the converging lens. (a) What is the focal length of the diverging lens? (b) What is the height of the final image? (c) Is the final image upright or inverted?

Problem 5

An object is located $16.0 \mathrm{cm}$ in front of a converging lens with focal length $12.0 \mathrm{cm} .$ To the right of the converging lens, separated by a distance of $20.0 \mathrm{cm},$ is a diverging lens of focal length $-10.0 \mathrm{cm} .$ Find the location of the final image by ray tracing and verify using the lens equations.

Problem 6

An object is located $10.0 \mathrm{cm}$ in front of a converging lens with focal length $12.0 \mathrm{cm} .$ To the right of the converging lens is a second converging lens, $30.0 \mathrm{cm}$ from the first lens, of focal length $10.0 \mathrm{cm} .$ Find the location of the final image by ray tracing and verify by using the lens equations.

Problem 8

Show that if two thin lenses are close together $(s,$ the distance between the lenses, is negligibly small), the two lenses can be replaced by a single equivalent lens with focal length $f_{\mathrm{eq}} .$ Find the value of $f_{\mathrm{eq}}$ in terms of $f_{1}$ and $f_{2}.$

Problem 9

Cameras You would like to project an upright image at a position $32.0 \mathrm{cm}$ to the right of an object. You have a converging lens with focal length $3.70 \mathrm{cm}$ located $6.00 \mathrm{cm}$ to the right of the object. By placing a second lens at $24.65 \mathrm{cm}$ to the right of the object, you obtain an image in the proper location. (a) What is the focal length of the second lens? (b) Is this lens converging or diverging? (c) What is the total magnification? (d) If the object is $12.0 \mathrm{cm}$ high, what is the image height?

Problem 9

You would like to project an upright image at a position $32.0 \mathrm{cm}$ to the right of an object. You have a converging lens with focal length $3.70 \mathrm{cm}$ located $6.00 \mathrm{cm}$ to the right of the object. By placing a second lens at $24.65 \mathrm{cm}$ to the right of the object, you obtain an image in the proper location. (a) What is the focal length of the second lens? (b) Is this lens converging or diverging? (c) What is the total magnification? (d) If the object is $12.0 \mathrm{cm}$ high, what is the image height?

Problem 10

You plan to project an inverted image $30.0 \mathrm{cm}$ to the right of an object. You have a diverging lens with focal length $-4.00 \mathrm{cm}$ located $6.00 \mathrm{cm}$ to the right of the object. Once you put a second lens at $18.0 \mathrm{cm}$ to the right of the object, you obtain an image in the proper location. (a) What is the focal length of the second lens? (b) Is this lens converging or diverging? (c) What is the total magnification? (d) If the object is $12.0 \mathrm{cm}$ high. what is the image height?