A First Course in Physics · Ch. XX, §§ 546–551 · Chapter 20: Formation of Images
64. Lenses and the lens formula
Goal: Your student can find a convex lens's focal length, describe the images it forms as an object moves, use 1/u + 1/v = 1/f with image-size ratios, and describe images in a concave lens.
You'll need
- The book, open to these pages
- A magnifying glass (convex lens)
- A white card or wall, a ruler, and a candle or small lamp in a darkened room (with an adult)
- A pair of glasses for nearsightedness if anyone has them (concave lenses)
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
A convex lens focuses sunlight; its focal length; the series of images from a convex lens (like a concave mirror); secondary foci at twice the focal length; image and object sizes; virtual images in a convex lens; concave lenses; the formulas 1/v = 1/u + 1/f and 1/u + 1/v = 1/f with a worked example. Sixteen problems follow.
The lesson, step by step
Hook question
SayHow does a magnifying glass make things look bigger, and how can the same lens throw an upside-down picture of a window onto the wall?
Read together
Read §§ 546–551. The book's summary:
We learn, then, that a convex lens forms a series of images which is identical with the series formed by a concave mirror.
Try it: a lens camera
Stand across the room from a bright window and hold the magnifying glass between the window and a white wall or card. Move it until a small, sharp, upside-down picture of the window appears. The lens-to-card distance is about the focal length. Then do the same with a candle or lamp across a dark room: move the lens to make the image larger or smaller (§ 547).
Safety: never look at the Sun through a lens, and never point a magnifying glass at the Sun near paper, skin or anything that can burn; a lens can focus sunlight hot enough to start a fire.
Try it: the magnifier
Hold the lens close to print: the letters look larger and upright (a virtual image, § 549). If you have glasses for nearsightedness, look through them at print: the letters look smaller (a concave lens, § 550).
Use the formula
For a convex lens or concave mirror: 1/u + 1/v = 1/f, where u is the object distance, v the image distance and f the focal length. Work the book's example: object 200 cm, image 50 cm: 1/200 + 1/50 = 1/40, so f = 40 cm. The image is to the object as v is to u.
(When the formula gives a negative v, the image is virtual, on the same side as the object.)
Say it back
Your student explains why an object at twice the focal length gives an image the same size, at the same distance on the other side.
Problems
Work problems 1–16 on book page 432; choose about ten if time is short (try 1, 2, 9, 10, 11, 13, 14, 15 and 16).
Afterwards
Use the magnifying glass to look closely at a leaf, salt grains and a fingerprint. Find its focal length again and compare with your first measurement.
Tip
Safety: never look at the Sun through a lens, and never point a magnifying glass at the Sun near paper, skin or anything that can burn; a lens can focus sunlight hot enough to start a fire.
Answers to the book's problems
1. 125 ft. 2. 2.25 in. 3. Its image lies on lines drawn to the center of curvature, which close in on each other as the object moves away. 4. The nose is nearer the mirror than the ears, so its image is relatively larger. 5. No; its images are always virtual and erect. 6. Real when the object is farther away than the focal length, virtual when nearer; enlarged when it is between the focus and twice the focal length (or inside the focus), diminished beyond twice the focal length; inverted when real, erect when virtual. 7. Erect, virtual and smaller than the object, because the lens always makes the waves spread more. 8. A real image is formed where the light actually meets and can be caught on a screen; a virtual image is only where the light seems to come from. 9. About 28.6 cm (focal length 14.3 cm). 10. The image is 2.5 times as large as the object. 11. Real, inverted, 60 cm from the lens and 4 times as large. 12. If u = v, then 2/u = 1/f, so u = 2f. 13. About 27.7 in. (about 2.3 ft.). 14. 1.8 in. 15. About 31.6 cm behind the mirror, virtual and erect, about 0.21 times the size of the object. 16. 120 cm behind the mirror, virtual and erect, 4 times the size of the object.
Worked out for this site from the scan. If a number in your copy differs, trust the book.