Problems

1. The sun is 60° above the horizon. Rays from the sun strike the still surface of a pond and cast a shadow of a stick that is stuck in the sandy bottom of the pond. If the stick is 10 cm tall, how long is the shadow?

2. On the Earth, you can see the ground in someoneâs shadow; on the moon, you canâtâthe shadow is deep black. Explain the difference.

3. If you hold a spoon in front of your face so that you see your image in the bowl of the spoon, your image is upright if you hold the spoon close to your face, inverted if you hold the spoon far away. Explain why this change occurs.

4. A 3.0-cm-tall object is 30 cm in front of a converging lens with a focal length of 10 cm. Draw a ray diagram to approximately determine the location of the image. Now, use the thin-lens equation to determine the location and height of the image.

5. A 2.0-cm-tall object is 15 cm in front of a converging lens that has a 20 cm focal length. Draw a ray diagram to approximately determine the location of the image. Now, use the thin-lens equations to determine the location and height of the image. 

6. 1.0-cm-tall object is 15 cm in front of a diverging lens that has a 30 cm focal length. Draw a ray diagram to approximately determine the location of the image. Now, use the thin-lens equations to determine the location and height of the image.

7. A typical diverging mirror on the passenger side of a car has a focal length of -80 cm. A 1.5-m-tall cyclist on a bicycle is 25 m from the mirror. Where does the image appear? What is the image height?

8. You are using a converging lens to look at a splinter in your finger. The lens has a 9.0 cm focal length, and you place the splinter 6.0 cm from the lens. How far from the lens is the image? What is the magnification?

9. The rod and cone cells in the central part of the retinaâthe foveaâare packed more closely, giving a more detailed view. This area of increased rod and cone density has a diameter of about 1.5 mm. When you read a book, you want the image of the text you are reading to fall on the fovea. If you hold a book 30 cm from your eyes, how wide is the spot on the page whose image just fills the fovea? That is, how wide an area do you see most clearly? Assume that the image on the retina forms 17 mm from the lens in the eye (which gives 1/sâ = 60. )

10. The moon is 3.5Ã10^6 m in diameter and 3.8Ã10^8 m from the earthâs surface. The 1.2-m-focal-length concave mirror of a telescope focuses an image of the moon onto a detector. What is the diameter of the moonâs image?

11. My friend Lisa admitted that she needed reading glasses when her near point got to be 60 cm. What power lens, in diopters, would she need to be able to see clearly at a more comfortable distance of 25 cm?

12. A jeweler is wearing a 20 D magnifying lens directly in front of his eye. If his near point is the typical 25 cm, how close can he hold a gem that he is inspecting?