College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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- Figure shows a simple version of a zoom lens. The converging lens has focal length f1 and the diverging lens has focal length f2 = -Ι f2Ι. The two lenses are separated by a variable distance d that is always less than f1. Also, the magnitude of the focal length of the diverging lens satisfies the inequalityΙ f2Ι7( f1 - d). To determine the effective focal length of the combination lens, consider a bundle of parallel rays of radius r0 entering the converging lens. (a) Show that the radius of the ray bundle decreases to r′ 0 = r0( f1 - d)/f1 at the point that it enters the diverging lens. (b) Show that the final image I′ is formed a distance s′ 2 =If2I( f1 - d)/(I f2I- f1 + d) to the right of the diverging lens. (c) If the rays that emerge from the diverging lens and reach the final image point are extended backward to the left of the diverging lens, they will eventually expand to the original radius r0 at some point Q. The distance from the final image I′ to the point Q is the…arrow_forwardAn object of height 10.0 cm is placed 20.0 cm away from a converging lens. The image is 30.0 cm high. One can conclude that the focal length of the lens can be (A) 12.0 cm only. (B) either 12.0 cm or 60.0 cm. (C) 15.0 cm only. (D) either 15.0 cm or 30.0 cm.arrow_forwardTwo lenses are placed along an optical rail. One is a converging lens, with a focal length of f1 = 30.3 cm. The second lens, a diverging lens with a focal length of f2 = −20.0 cm, is placed d = 110 cm to the right of the converging lens. An object ho = 2.02 cm high is placed p1 = 40.5 cm to the left of the converging lens. (a) Determine the position of the final image. (Enter the position in cm relative to the diverging lens.) magnitude ? cm direction right or left? of the diverging lens (b) Determine the magnification of the final image. (Indicate the orientation with the sign of your answer.) Hint* The total magnification is the product of each individual magnification. (c) Is the image upright or inverted? (d) Repeat parts (a) through (c) for the case in which the second lens is a converging lens having a focal length of 20.0 cm. (Enter the position in cm relative to the second lens. Indicate the orientation of the magnification with the sign of your…arrow_forward
- You want to purchase a microscope for doing surgeries, which requires that there is at least 10cm distance between the objective lens and the patient. The objective forms a highly magnified real image of the object at a distance L. You want the image to look 50 times larger. What should be focal lengths of the objective and the eye piece assuming L=200mmarrow_forwardOn one side of a diverging lens of focal length 59.0 cm, you position an object of height 3.92 cm somewhere along the principal axis. The resultant image has a height of 2.74 cm. How far from the lens is the object located? 17.8 cm 25.4 cm 43.2 cm 33.0 cmarrow_forwardCompute the focal length of a diverging thin lens made of flint glass, whose refractive index is 1.66 and is immersed in air having refractive index 1. The radii of the spherical surfaces of the lens are 10 cm and 20 cm. Select one: O -30 cm O O -10 cm 30 cm 10 cmarrow_forward
- What is the focal length of the lens in your eye when you can focus on an object at your near point? Assume that the distance from your lens to the back of your eye is 2.0 cm, that your near point is 21 cm in front of your lens, and that the liquid behind the lens has n=1.00 just like the air in front of your lens. (a) 1.8 cm (b) 18 cm (c) 2.1 cm (d) 21 cm (e) None of the above.arrow_forwardIt is your first day at work as a summer intern at an optics company. Your supervisor hands you a diverging lens and asks you to measure its focal length. You know that with a converging lens, you can measure the focal length by placing an object a distance ss to the left of the lens, far enough from the lens for the image to be real, and viewing the image on a screen that is to the right of the lens. By adjusting the position of the screen until the image is in sharp focus, you can determine the image distance s′s′ and then use the equation 1s+1s′=1f1s+1s′=1f, to calculate the focal length ff of the lens. But this procedure won't work with a diverging lens−−by itself, a diverging lens produces only virtual images, which can't be projected onto a screen. Therefore, to determine the focal length of a diverging lens, you do the following: First you take a converging lens and measure that, for an object 20.0 cmcm to the left of the lens, the image is 29.7 cmcm to the right of the lens.…arrow_forwardA 1.00-cm-high object is placed 3.95 cm to the left of a converging lens of focal length 7.80 cm. A diverging lens of focal length –16.00 cm is 6.00 cm to the right of the converging lens. Find the position and height of the final image. position 7.5 cm in front of the second lens v 0.5466 height Calculate the magnification produced by each lens. Then consider how the magnification relates image size and object size for each lens to find the height of the final image. cm Is the image inverted or upright? upright O inverted Is the image real or virtual? real virtualarrow_forward
- The distance between the eyepiece and the objective lens in a certain compound microscope is 10.4 cm. The focal length of the objective is 0.430 cm, and that of the eyepiece is 1.40 cm. Find the overall magnification of the microscope. (The near point of the eye is 25 cm. Assume that the object is placed at the focal point of the objective lens, and one places the eyepiece at the near point of the eye.)arrow_forwardYou want to make a symmetrical biconvex lens (same radii of curvature) to project an image of an object magnified five times on a wall 40 cm away from the lens. The material has an index of refraction equal to 1.60.(c) What is the radius of curvature of the lens faces? 12 cm 8 cm 4 cm 10 cm 2 cm 6 cm (a) What is the distance from the object to the wall? (b) What is the focal length of the lens? (a) 8 cm (b) 6,67 cm (a) 18 cm (b) 6,67 cm (a) 28 cm (b) 6,67 cm (a) 48 cm (b) 6,67 cm (a) 8 cm (b) 8,00 cm (a) 18 cm (b) 8,00 cm (a) 28 cm (b) 8,00 cm (a) 48 cm (b) 8,00 cm (a) 8 cm (b) 9,67 cm (a) 18 cm (b) 9,67 cm (a) 28 cm (b) 9,67 cm (a) 48 cm (b) 9,67 cmarrow_forwardA laser beam of diameter d₁-1.1 mm is directed along the optical axis of a thin lens of focal length +4.7 cm (see figure below). (a) How far from the lens will the beam be focused? (b) A second positive lens is placed to the right of the first. Light emerges from the second lens in a parallel beam of diameter dy 3.6 mm. Thus the combination of lenses acts as a beam expander. Find the focal length of the second lens. Find the distance between the lenses.arrow_forward
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