E.J. Zita, April 1998
Adapted from Grinnell optics workshops, Phil Pearl's thin lense workshop, and Ferguson's telescope workshop.
(A) By holding a lens at the window, and placing a screen behind the lens at the focal distance, you can see that a real image appears on the screen.
(B) 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. Make one.
(C) Play with different lenses and investigate how the relative positions (and focal lengths) of lenses affect image locations and sizes, if you have time.
This workshop is designed to let you see how lenses affect light. By bending light rays, lenses can focus light (onto camera film...), form images (on your retina...), defocus light (useful in some corrective lenses), and change the sizes of images (telescopes, microscopes...) Do parts A and B; 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!
Equipment:
The focal length (f, or focal point) of a lens is half the radius of curvature R of the lens. The focal length is also the point at which the lens will focus distant light (parallel rays) into an image. For example, light bounces off a tree 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 card to that point, you can see that the focused rays form an image (on the card) of your object (the tree).
Measure the focal lengths of several lenses: Choose convex lenses. You can feel that they curve out, not in (concave), on both sides, even if you can't see the curvature. Go outside or to the window. Choose a distant object such as a tree. Holding a lens in one hand and a 3x5 card in the other, and vary the distance between them until a clear image forms on the card. Is the image upright or inverted? Grey or in color? Light rays actually converge in space at the position of this image, so we call it 'real'. The screen reflects these light rays into your eyes. Have a partner measure the distance between the card and the (center of) the lens. Keep track of which lens has which focal length.
Imagine putting camera film or your retina in place of the card. The light of the image elicits an electromagnetic or chemical response from the surface it falls on. Notice that the point where objects focus appears independent of their color or size.
Get two convex lenses, one highly curved (small f: the eyepiece) and a flatter one, with a very slight curve (large f: the objective). Fix the objective on the optical bench and use your 3x5 card to find the image of a distant object (e.g. an illuminated wall clock inside, if trees outside are too dim). Then put a magnifying glass or eyepiece lens in place of the card, at the original image location. This will direct the image light into your eyes as parallel rays. Does it look like the object is closer or further? Larger or smaller? Move the lens and your eye around, and convince yourself that eyepiece must be placed behind the real image for you to see it.
Magnification: Try to see the clock itself in the same field of view as your magnified image of the clock. Estimate how much bigger the image is. The ratio M= (-image size/ object size) is the magnification. Compare M to the ratio of your lenses' focal lengths.
(C.1) 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. Mount a light 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 arrow light. What is its focal length f? (a) Move the lens and/or the card around until you get a clear image of the arrow on the card. Measure the object distance, p, between the object and the lens, and the image distance, q, between the object and the lens, and keep track of them. (b) Move the lens away from the light (increase p). Where do you have to move the card to find the image? Does q increase or decrease? Does the image get bigger or smaller?
(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 you got in part (1)?
(C.3) Magnification M=-q/p = relative size of image, compared to object. 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 (say 10 cm) from your arrow light. 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?