Procedure and Questions In recording your observations and perform- ing calculations you must get the signs of the d's and it's eorrmt. For object and image dis- tances, follow the sign conventions given pre- viously. For it's, an upright object or image is taken as positive and downward or upside down object or image is taken as negative. if the image is faint, you may need to work in a darkened room. Working in the evening with minimal room ghting may be a solution. Object at innity 1. Measure the object size lirafrom the base of the arrow to its tip. Record this value at the top of the data. sheets. 2- For this rst activity you will need to move your object [colored arrow on ash- light} at least ve meters from the lens and point the beam at the lens. {The source doesn't have to he at the same height as the lens for this part. it can be higher or lower by up to 50 cm and will have virtually no effect on the mea- surements.) Move the screen to create an image of the far away object on it and record the po- sitions of the lens and image to nd the image distance di (or simply measure this distance directly}. The magnication will be mueh less than one1 i.e., the image will be much smaller than the object. indeed, it's not easy to see the arrow. it may ap- pear to be only a small sharp spot1 but if you look closely you should he just about able to see the colored arrow in the small spot of light. at the TV or window with the imaging screen behind it showing an upside down image. 3. Answer Comprehension Questions 1. Image at innity The arrangement for \"image at innity\" is similar to that of the previous experiment if the directions of the rays were reversrxl with the image becoming the object and the object becoming the image. It is the basic principle behind a movie theater projector where the object [the lm) is brightly illuminated from behind by the projector light bulb. A non- verging lens in the. projector produces a real image (the movie picture) very far away {on the movie screen). 4. For this activity, the image screen should be a light colored wall at least two meters away and preferably more than four me- ters away. The image will be quite large and therefore quite dim, so you will need a darkened room just to see it. You may need to do this at night to get the room dark enough. 5. Place the lens near the source and move it away until an image forms on the wall. Emord the object and lens positions In and ac,- to nd the object distance or mea- sure the object distance do directly. 6. Answer Comprehension Question 2. Converging Lens 7. Tape down the tape measure in a posi- tion that will make for easy position mea- surements of the object, lens, and screen. 12 9. The source will stay xed but. the lens and screen will be moving a hit for the activities to follow. Try to position the ashlight so that the arrow is accurately positioned at one of the 10 cm marks on the tape measure and pointing straight along the tape measure toward the lens and screen. Use a. separate ruler when measuring the size of the image on the screen. Or, mark a scrap of paper to show the image size and measure that on the tape measure. Set the distance between the object and the screen to 100 cm. Record the object position so and the screen position 3:,- on the data sheets. Position the lens midway lmtween the ob- ject and the screen and move it toward the object until an enlarged image of the arrow forms on the screen. Move the lens (keeping it perpendicular) to get the sharpest possible image. Measure and record the lens position 53;. Remember to measure to the middie of the lens, which is not easy with the lens mount getting in the way. if it helps, you can measure to the front surface of the lens and adjust the position by 0.75 cm to take into ac- count that the lens is 1.5 cm thick in the middle. 10. 11. 12. 13. Introductory Physics Laboratory Measure and record the size it; of the im- age. Reposition the lens midway,r between the object and the screen, but this time move it toward the screen until a reduced im- age of the arrow is formed on the screen. Again measure and record .12; and in. For each of the two images just observed, determine do and (1;; determine the mag- nication M from M = Iii/ho; determine Mpm from d,- and do ($1.2); and deter- mine the focal length 1' from at; and :1.- (Eq. 1). Continue on at Comprehension Ques- tions 3 leaving the optical components as they are currently arranged with the ob- ject, lens, and screen arranged to produce a redueed, real image on the screen. 2 cm Object size: ho = Object at infinity 55 cm Object distance: do = Image distance: di = 35 cm Image at infinity 55 cm Object distance: da = _ Image distance: di=- 35 cm Converging Lens Object size: ho 2 cm 10 Object position: I= 110 Screen position:Object at infinity; Image at infinity 1. For an object truly at infinity (do = co), explain why the lens equation (Eq. 1) predicts that f = d; and give your measured value for di. Focal length assuming do = co: di = Instead of assuming do = co, measure the actual object distance as best you can and use this value for do to recalculate f using Eq. 1. Focal length using do = For a large but finite object distance is the image: at the focal point of the lens, just inside the focal point (nearer the lens), or just outside the focal point? Le., is d; predicted to be bigger, smaller, or equal to f? Use Eq. 2 with your measured ho, d, and d;, to predict the size of the image. Image size predicted: hi = Does the predicted image size agree with your observations? You don't have to measure the image size. Just check if it is in reasonable agreement with your prediction. Does the sign of the predicted magnification agree with the direction of arrow in the image, i.c., whether it is erect or inverted?2. For an image truly at infinity (d; = co), explain why the lens equation (Eq. 1) predicts that do = f and give your measured value for do. Focal length assuming d; = co: do =. Instead of assuming di = co, measure the actual image distance as best you can and use this value for d; to recalculate f. Focal length using di f =. For large image distances d; > f, is the object expected to be just inside, just outside or at the focal plane? That is, is do predicted to be bigger, smaller, or equal to f? Use Eq. 2 with your measured ho, do and di, to predict the size of the image. Image size predicted: hi = . Does the predicted image size agree with your observations? You don't have to measure the image size. Just check if it is in reasonable agreement with your prediction. Does the sign of the predicted magnification agree with the direction of arrow in the image, i.c., whether it is erect or inverted?Converging Lens 3. What pattern can you observe between the two sets of values for d, and d; for the two cases? What is the product of the two measured magnifications? How are the answers to these questions related to the behavior of Eqs. 1-3 if the values of d, and d; are swapped? 4. Compare the four focal length determinations made so far. According to the manufacturer, these lenses are designed to have a focal length of 20 cm. Do your measurements agree? 5. With the reduced image displayed on the screen, predict what will happen if you block the top half of the lens with your hand. Prediction: Now try it. Also observe what happens when you block the bottom half of the lens. Describe the changes to the image. Description:The focusing properties illustrated in Fig. 1 can be used to show that all paraxial rays emitted from a point a distance d, from the lens (and going through the lens) converge to a point a distance d; from the lens where d; is related to do and f by the "Thin Lens Equa- tion" d (1) Additionally, the values of h; and h, are re- lated by hi di do (2) ho For Fig. 2, do and d; are positive, and the negative sign in Eq. 2 indicates that with ho being positive, i.c., above the optic axis, h; will be negative, i.e., below the optic axis. Eq. 2 is easily derived using the similar tri- angles (darkened in the figure) including the indeflected ray along the optic axis. The quantity h;/hy-the ratio of the image size to the object size is called the magnifi- cation and is denoted M. M = hi ho (3)