Objectives 1. Introduce the Thin Lens Equation and Magnification calculations for simple optical systems 2. Investigate

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Objectives 1 Introduce The Thin Lens Equation And Magnification Calculations For Simple Optical Systems 2 Investigate 1 (90.5 KiB) Viewed 34 times

Objectives 1 Introduce The Thin Lens Equation And Magnification Calculations For Simple Optical Systems 2 Investigate 2 (75.08 KiB) Viewed 34 times

Objectives 1 Introduce The Thin Lens Equation And Magnification Calculations For Simple Optical Systems 2 Investigate 3 (75.21 KiB) Viewed 34 times

Objectives 1 Introduce The Thin Lens Equation And Magnification Calculations For Simple Optical Systems 2 Investigate 4 (30.13 KiB) Viewed 34 times

Objectives 1 Introduce The Thin Lens Equation And Magnification Calculations For Simple Optical Systems 2 Investigate 5 (20.7 KiB) Viewed 34 times

Objectives 1. Introduce the Thin Lens Equation and Magnification calculations for simple optical systems 2. Investigate and verify the Thin Lens and Magnification equations 3. Experimentally determine the focal length and magnification of a convex (converging) lens (lab report) 4. Experimentally determine the focal length and magnification of a concave (diverging) lens Materials & Resources 1. Optics track, light source, view screen, ruler, and a convex and concave lens Introduction Recall from a previous lab that the main property of a lens is its focal length, which results from the shape of the lens (its radius of curvature for a spherical lens) and the index of refraction of the material it's composed of. But lenses are used all the time to change the way objects look; think of glasses, telescopes, microscopes, and any number of other common optical devices. The relation between how a lens is made (its focal length) and what it does (changes the way objects appear) is given by the Thin Lens equation: 1 1 1 f where s, sand / are the object distance, the image distance, and the focal length, respectively, where all are measured from the center of the thin lens. Note that this equation is for thin lenses only; the equation for describing lenses in general is a bit more complicated because the path of the light through the lens itself is too long to neglect. But, this equation is valid for both convex (converging, positive focal length) and concave (diverging, negative focal length) thin lenses. Another property of lenses is magnification, which represents how large or small an object looks when viewed through a particular lens. Magnification is defined as the ratio of an object's image height, h', to its actual height, h, and is expressed as: hi - + = S MA h When the image looks smaller than the actual object, the magnification is less than 1, but when the image looks larger, or is magnified, the magnification is more than 1. Another expression for the magnification of a lens is given by: M s! Figure 1 Note that when M has a negative value, the image created by the lens will be inverted, but if M is a positive value, then the image created will have the same vertical orientation as the original object. In the experiment below, if the image is found to be inverted, then the image height, h must be expressed as negative. This equation can also be used for more than one simple lens, or a compound lens just use it normally for the first lens, but for the second lens the image from the first lens must be used as the object for the second lens. The magnification of a compound lens is given by the product of the magnification of each individual lens. In this lab, we will only use two lenses, so: MT= MM

1. The Focal Length and Magnification of a Converging, Convex Lens (Lab Report) f-Sitesi Procedure lens Screen mag Lightere (object) 1) Attach the light source to one end of the optics track as shown in Figure 2. Carefully place --> Miche the convex lens in the lens mount and verify Oh Image that the lens is as close to centered in the lens mount as possible. Attach the lens mount to the optics rail so that the center of the lens is Figure 2 10 cm from the light source (object). 2) Attach the screen to the end of the bench opposite the light source. This will be where the image of the lens is projected. Slide the screen back and forth on the rail until the projected image becomes clearly focused. Once acle image is obtained, measure the image distances from the center of the lens, and then calculate the magnification de and the focal length using the thin lens equation record your results in the table below. Note: it may not be possib to obtain a clear image for every distance in the table. If so, record "no image in the image description column. 3) Measure the object height h and the image height h, calculate the magnification Me, and then describe the image as either magnified or reduced, as well as upright or inverted in the table below. S.S 4) Repeat steps 1-3 for each object distance listed in the table. Object Image Magnification Focal Object Image Magnification Image Distance, Distance, M.-'' Length Heighth Heighth MA- Description 15 -0.25 la .4 0 Clear -0,32 1.12 니 1 0.25 clear 17 -0.425/11.93 4 1.5 0.375 clear 19 - 6.63 11.63 4 2.5 0.625 clear 29 -1.45 11.84 4 16.a 1.55 clear NA NA NA 4 NA NA 5) Open Capstone and select "Enter Data" on the welcome pop-up. Enter your values for f in the "X" column and find the mean and standard deviation for the focal length of the lens using the drop-down (DO NOT include the Sem object distance result). Calculate the percent error in f using an accepted value of 10.0 cm. Record your results below and print the completed table for your report, +48- 11.90 0.18 ) % Error in Questions: 14 60 cm 50 cm 40 cm 30 cm 20 cm 5 cm Ino image 1) Briefly explain why it is not possible to obtain an image at all of the object distances in the table? not all of the mags product a clear image. 2) Is your value for highet or lower (cirete one) than the accepted value /- 10.00 cm?higher 3) What does this result say about the radius of curvature of the lens? 4) What does the higher or lowetſ say about the distance measurements that were made? 5) Based on the uncertainties of the distance and height measurements made in this experiment, which representation of the lens' magnification is more accurate, M. or Me (circle one)? Justify your answer below. 2

Object distance 3: _11.5cm 2. The Focal Length and Magnification of a Diverging, Concave Lens Background Recall from last week that the focal point of a concave lens is on the same side as the light source. This where h'=h; means that image produced by a concave lens is a virtual image. As such, no screen can be used to locate the image without blocking the creation of the log image, and the previous procedure for finding the focal length and magnification of a convex lens will Si not work for a concave lens. However, it is possible to $ calculate the focal length and magnification of a concave lens by including it in a compound lens with a Figure 3 convex lens and measuring the focal lengths and magnifications of the convex and compound lenses Procedure 1) Setup the light source on the optics rail as shown above 88.5 cm Image distances In this case, place the convex lens about 17.5 cm from the light source, which is about between the focal length 10.0 cm and 2/ -20,0 cm Object height : 2) Adjust the screen until the image comes into focus and Image height_9cm then measure the image distance, the object height and the image height : Calculate the magnification of Magnification direct method): the lens Musing both equations and record the results. Mihilh 2.25cm Note: both magnification here should be the same value 3) Insert the concave (diverging) lens about halfway between Magnification (distance ratio) the convex lens and screen. Adjust the screen until the Mi-sits, a.acmi image comes into focus. Carefully make the remaining measurements, as illustrated in Figure 3 above, Lens separation, r. 18,5cm 4) Calculate the magnification M, and the focal length of the concave lens using the formulas given below, and then Second lens image distance: 55 - 19cm calculate the percent error in your measurement of using Second lens object distance the accepted value of 10 cm. Show your percent error $-3--:_lom calculation in the space provided to the right 2 Image height is: 12 cm Magnification, M, --5/ -19 Focal length. fs = 3:53+(2+s4: 0.95 % Error in 5) Calculate the total magnification of the compound lens using the formulas given below for Mr and Mt, and then calculate the percent difference between those values. Show your percent difference calculation in the space below, Direct measurement: Mr = h'/h Distance Ratio: M = (-35) - % Difference in MDF 9 Questions 1) Are your experimental values for the magnification of the compound lens Mr and Ms approximately cqual? 2) Which value Mas or Mo (circle one) is a reliable representation of the magnification of the compound lens? Why? 3) Is your experimental value for the focal length of the diverging lens f higher or lower (circle one) than the accepted value? Give a physical explanation of this experimental result below. 3

70 ETUI Questions: 1) Briefly explain why it is not possible to obtain an image at all of the object distances in the table? not all of the images product a clear image. 2) Is your value for higher or lower (circle one) than the accepted value f-10.00 cm? 3) What does this result say about the radius of curvature of the lens? om? higher 4) What does the higher or lowerf say about the distance measurements that were made? 5) Based on the uncertainties of the distance and height measurements made in this experiment, which representation of the lens' magnification is more accurate, M. or Mx (circle one)? Justify your answer below.

Questions: 1) Are your experimental values for the magnification of the compound lens Mr. and Mr. approximately equal? 2) Which value Moor Mn (circle one) is a reliable representation of the magnification of the compound lens? Why? 3) Is your experimental value for the focal length of the diverging lens higher or lower (circle one) than the accepted value? Give a physical explanation of this experimental result below. 3