Physics 2020 Lab 8 Lenses Name Section Introduction. In this lab, you will study converging lenses. There are a number of different types of converging lenses, but all of them are thicker in the middle than at the edges. A common converging lens shape is shown to the right. We don t expect that you have studied lenses in class yet today s lab will be an experimental introduction. Tues Wed Thu 8am 10am 12pm 2pm 4pm f Figure 1 When a bundle of parallel light rays enters a converging lens (see above), the rays are focused onto a point in space (called a focal point of the lens) at a distance we call f (the focal length), from the lens. Conversely, if a point-like light source is located at a focal point of the lens, the rays that enter the lens will be bent into a parallel outgoing bundle just reverse the arrows in the figure above! Convince yourself that the picture to the right is showing this same idea as the ray reversal of the top figure We can think of the focal point as existing symmetrically on both sides of the lens (same f on either side) - light rays are reversible. f Part I: Image Formation Figure 2 A. In the figure below, draw rays of light coming from the tip of the arrow-shaped object and going out in many directions. Next, draw rays of light coming from the middle of the object going out in many directions. If you were to expose a piece of photographic film to this mess of rays at some distance away, what would it look like? Page 1
B. Now we put a lens in place. The points labeled F are the focal points (the distance from the center of the lens along the optical axis to either of the points F is f, the focal length). We have labeled the distance of the object (the big arrow on the left) from the lens as the object distance, or d o. Three different rays originating from the tip of the object to the lens are shown. (There are infinitely many more, but we don t want to overcomplicate the picture) Draw carefully (use straightedges) how these rays continue after they go through the lens (Hint: Both figures in the Introduction should help! Follow those rules, don t guess where the rays should go!) The one ray here that the introduction does not directly help with is the middle ray, the one going to the center of the lens. But, any ray that approaches the center of a symmetric lens like this continues straight on through, unbent! Do the rays meet at (approximately) one point on the other side of the lens? (They should! But, that point is NOT necessarily located a horizontal distance f from the lens.) Draw another three rays originating from the middle of the object (one parallel to the optical axis, one through the center of the lens and one through the focal point on the same side of the lens as the object). Do these rays meet at one point? Check your drawing with your TA. Page 2
C. You should have found that all light rays that originate from any ONE specific point on the object and then go through the lens are redirected to arrive at ONE single point, an image point. All these points together then form a complete image of the object on the other side of the lens. Draw/show the image in the figure on the previous page. How does it compare with the original object? If you expose a piece of film to the rays arriving at the image location, what would it look like? D. Now suppose we remove the lens (returning to the situation described in part A.) Would the light rays coming from the object still form an image, like they did in part B? Does this agree with your answer to the question in part A? Part II: Measuring Focal Length with a Collimated Beam The optics bench is a rail on which lenses are placed, with a ruler on the side (for measuring distances.) The other equipment we have includes a small bright light, which acts almost like a point source and three converging lenses labeled A (Red), B (White), and C (Blue). There is a piece of paper, which will act as a screen to view images. Finally, there is paper with an aperture (a hole) in the shape of a butterfly. The hole is covered with a frosted, translucent material (scotch tape). When this aperture is placed in front of the little light source, it forms a convenient object for image-forming experiments, like the arrow in part I. A. Your goal in this part of the lab is to set up your equipment so it matches the second picture in the introduction: a point-source located on the optical axis, exactly one focal length f to the left of a lens. The beam on the other side of the lens is called a collimated beam. (Remove the butterfly outline from the light source. The source itself is very small and can be considered to be a point source.) Adjust its position so that the source is at the edge of the meter stick. Now place lens A close to the source and slide it away until it produces a parallel, collimated beam: Discuss with your partners the best way to check that the collimated beam is (reasonably) parallel, and then try it! Describe your choice of procedure here: Page 3
Why does your collimated beam produce a disc of light? You should have adjusted the position of lens A so that the diameter of the disc of light, far away, is the same as the lens size. Measure the distance from the point source to the lens; this is the focal length f A. (Do you see why? Redraw the picture from the introduction if it s not obvious to you ) Record the focal length of lens A here: B. If a point source and a lens have been set up to produce a collimated beam (i.e. parallel rays), then the focal length of another lens can be easily measured! The second lens (lens B) is placed in the collimated beam, and the place where the rays are brought to focus is measured. The distance from lens B to the focal point is f B, the focal length of lens B. point source f A fb lens A lens B screen Does it matter how far away you place lens B from lens A in this setup? (Will this choice impact your measurement of the focal length of lens B?) Try it out with your equipment! Use this method to measure the focal lengths of lens B. (Without moving lens A, place lens B just beyond A, at a convenient integer mark, and put the paper screen beyond B. Now move the screen until you get a sharp image of the point source on the screen. The distance from lens B to the screen is f B.) Record it here: Repeat the previous step with lens C in place of lens B. Record the focal length of lens C below: Page 4
Part III: Measuring Focal Length by Image Formation Let s return all the way back to part I-B, where we had a single object a distance d o to the left of a lens. (In that part, note that d o was NOT the focal distance, it was farther than f.) Back in I-B, you should have found an image somewhere off to the right of the lens. (but again, NOT a distance f away!) We call the distance from the lens to the image: d i ( image distance ). A. It is not obvious (!) but we can (and will, in lecture) work out that the focal length f of a lens, the object distance from the lens d # and the image location d $ are related by the lens equation: 1 1 1 = + f d0 d i The object distance d # and the focal length f were given in the figure from I-B (on page 2) Clearly label the image distance, d i, in the same figure (back on page 2). If you could measure d # and d $ in the lab, can you use the lens equation to determine the focal length (f) of a lens? (How?) Let s try it: place the light source at the end of the optics bench and place the Scotch tape diffuser in front of it. Place the butterfly aperture on the front of the light source. It will save a little trouble in your calculations if you position the source so that the object (the butterfly) is exactly beside an integer mark (e.g. 2.0 cm) on the scale of the bench. Record the position of the object: Turn on the light source. Place the paper screen, I, at the far end of the bench. Again, it will save some trouble if you locate it a convenient integer mark, like 90.0 cm or 92.0 cm. Record its position. B. Now put lens B on the bench close to the object (the butterfly) and move it slowly away from the source until you see a clear image on the screen. The image is most easily seen looking through the screen towards the light source, but it can also be seen from the other side. Adjust the position of the lens to give the sharpest image and record the position of the lens (as indicated by the ring on the housing). Page 5
Draw a sketch of the setup you have constructed, clearly labeling the appropriate parts. (The figure we drew on Page 2 may serve as a template) Measure d # and d $ and record them below. From the lens equation, calculate the focal length f. How does the focal length for this lens compare with what you measured using the (very different) collimation method of part II? Repeat the procedure with lens A, and again compute the focal length of lens A with the lens equation method. Record your data and calculations here (and again compare with part II) Do you think the lens equation method is more or less accurate than the collimated beam method? Why? (Your TA might have nominal values for the focal length of the lenses) Page 6
C. Swap back to lens B, and restore a nice sharp image on the paper screen. If the image is at this point not centered on the screen, adjust the position of the object plate on the front of the light source until the image is centered. Then: As best you can, measure h 0 and h i, the heights of the object and image, and record them below. Compute M hi =. We call this ratio the Magnification (why?) h 0 Also compute the value d i. d 0 Are the two ratios you just computed (roughly) the same? Draw a clear picture - can you see any geometrical reason why they should be the same? D. What do you expect will happen to the image if you block half of the lens? Look at your diagram (way back on page 2) and imagine blocking half of the rays that are going through the lens. Would you still form an image? Would there be any differences? Try it! Block half of the lens with a piece of paper. What happens to the image? (Block the top half, or one side. Block MORE than half Mess about a little). Page 7
Connecting parts II and III mathematically: If d $ were set to in the lens equation, and we could measure d #, how could we determine the focal length f? What do you think the rays of light would look like near the lens if we said the rays converged to an image at infinity? Make a diagram, indicating a lens, and the rays which emerge from a point at a distance d 0 on the left side and then form an image at infinity on the other. Indicate focal length f on the figure. How is the lens equation used in this situation (mathematically) to determine f? Practice Exam questions (if you have time) An object is 6 cm in front of a small converging lens with focal length 2 cm. The object has height 3 cm, and the lens has a radius of 1 cm. The observer is off to the right. object d o =6 cm f=2 cm 1. The distance of the image from the lens is... A) 6 cm B) 5 cm C) 4 cm D) 3 cm E) None of the above is correct! 1 cm 2. The image is... A) to the left of the lens B) to the right of the lens (In class we will learn the terminology real and virtual images. You might start to think about which of these you would call this particular image!) 3. Compared to the object, the image is... A) shrunk (smaller than the object), and upright B) shrunk, and inverted C) enlarged (bigger than the object), and inverted D) enlarged, and upright E) A complete image is never formed, since the lens is smaller than the object! 4. If the object in the figure above is moved just slightly closer to the lens, what happens to the image? A) It moves closer to the lens AND it gets smaller B) It moves closer to the lens AND it gets larger C) It moves farther from the lens AND it gets smaller D) It moves farther from the lens AND it gets larger E) It does not change Page 8