Do parts A and B below; leave C for the very end in case you have extra time, maybe design some investigations of your own... and turn in the survey before you leave. Have fun!
(B) Make a telescope: If you remove the screen, the real image is still there in space, and it can be examined with a magnifying glass. That is a telescope.
(C) Further investigations: Play with different lenses. If you have time, investigate how the relative positions (and focal lengths) of lenses affect image locations and sizes, more carefully and quantitatively.
Light bounces off a tree (for example) in all directions. The few light rays that reach you from a distant tree are traveling nearly parallel to each other. When those parallel rays come through your lens, the lens will focus them at some point in space. If you move a blank card to that point, you can see that the focused rays form an image (on the card) of your object (the tree). The focal length is the point at which the lens will focus distant light (parallel rays) into an image. The focal length (f, or focal point) of a lens turns out to be half the radius of curvature R of the lens (Fig.a).
9Fig.(a) Convex lens | Fig.(b) Refracting telescope made of two convex lenses |
Measure the focal lengths of several lenses: Choose convex lenses to start with. You can feel that they curve out, not in (concave), on both sides, even if you can't see the curvature.
Magnification: Try to see the clock itself in the same field of view as your magnified image of the clock, one with each eye. Estimate how much bigger the image appears than the object. The ratio M= (-image size/ object size) is the magnification. (The minus sign is for the orientation of the image: is it right side up or upside down?)
How does M compare to the ratio of your lenses' focal lengths?
Extra: look through your neighbors' telescopes. How does their magnification compare with yours? What does this have to do with the ratio of the focal lengths of their lenses?
(C.0) It's also possible to make a telescope with a concave eyepiece. Try it if you have time. What size works for your objective? Do you notice any difference in the image?
(C.1) You have seen that images of distant objects form at the focal point of a lens. Images of close objects form not at the focal point, but at a point that depends on the distance between the object and the lens. The lighted arrows are convenient objects for investigating this. Mount a lighted arrow on one end of the optical bench, and a card on the other (no lens yet). Move the card back and forth; can you get an image of the arrow to focus clearly on the card? Now choose a lens to mount between the card and the lighted arrow, at some arbitrary distance.(C.2) Thin lens equation: (1/f) = (1/p) + (1/q)
Check this relation by calculating (1/p) + (1/q) for (a) and (b) above. How do your results compare to the focal length f of your lens? The results may not match perfectly. Why not?
(C.3) Magnification M=(-q/p) = relative size of image, compared to object, as you may have discovered above. Since the image and the object subtend the same angle from the lens, the larger is further away. An object close (small p) to the lens (but not inside the focal length...) yields a large image (large q) far from the lens (consider a magnifying glass). An object far from the lens (large p) yields a small image close to the lens (small q). Calculate the magnification M for your setup above. How does it compare to your observations about the relative size of the image and object, and their respective distances from the lens?
(C.4) Signs: Your p and q (and f) are positive numbers (for real objects and images, and converging lenses), so your M is negative. Does negative M correspond to an upright or inverted image?
(C.5) Predictions and tests: Pick a different lens whose f you know. Mount it a fixed distance p (greater than f) from your lighted arrow. Use the simple equation above to predict where the image will be (calculate q). Check your prediction by moving the card around until you find the image, to measure q. How do your results compare? How does the magnification change? What could contribute to a slight mismatch between your calculations and your observations?