Homework 10

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Louisiana State University *

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2002

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Physics

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Dec 6, 2023

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Homework 10 1. Two converging lenses have the sane focal length of 5.00 cm. They have a common principal axis and are separated by 22.0 cm. An object is located 10.0 cm to the left of the left-hand lens. What is the image distance (relative to the lends on the right) of the final image produced by this two-lens system? 2. A nearsighted person wears glasses to correct the problem. The lenses in the glasses have a focal length of -392 cm are are worn 2.0 cm fom the eyes. With the glasses, the person can see an object clearly that is very far away. How far from the eyes is the person’s far point located? 3. An object is located 99 cm in front of a converging lens (f= 66 cm). Determine where the image is located.

4. When a diverging lens is held 11.9 cm above a line of pint, as shown in the figure below, the image is 4.9 cm beneath the lens. (a)Is the image real or virtual? (b) What is the focal length of the lens? 5. (a) For a diverging lens (f= -22.0 cm), find the image distance for an object that is 22.0 cm from the les. (b) Determine the magnification of the lens. 6. The distance between an object and its image formed by a diverging lens is 11.0 cm. The focal length of the lens is -4.30 cm. Find (a) the image distance and (b) the object distance.

7. An object is 22 cm in front of a diverging lens that has a focal length of -17 cm. How far in front of the lens should the object be placed so that the size of its image is reduced by a factor of 1.9? 8. Two identical diverging lenses are separated by 20 cm. The focal length of each lens is -6.8 cm. An object is located 4.7 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right. 9. Two converging lenses are separated by 21.0 cm. The focal length of each lens is 8.20 cm. An object is placed 40.0 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right.

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10. A student is reading a lecture written on a blackboard. The lenses in her eyes have a refractive power of 60.25 diopters, and the lens-to-retina distance is 1.694 cm. (a) How far is the blackboard from her eyes? (b) If the writing on the blackboard is 5.01 cm high, what is the height of the image on her retina? 11. A woman can read the large print in a newspaper only when it is at a distance of 60 cm or more from her eyes. (a) Is she nearsighted (myopic) or farsighted (hyperopic), and what kind of lens is used in her glasses to correct her eyesight? (b) What should be the refractive power (in diopters) of her glasses (worn 2.4 cm from the eyes), so she can read the newspaper at a distance of 27 cm from the eyes? 12. The far point of a nearsighted person is 7.1 m from her eyes, and she wears contacts that enable her to see distant objects clearly. A tree is 23.3 m away and 1.7 m high. (a) When she looks through the contacts at the tree, what is its image distance? (b) How high is the image formed by the contacts?

13. The two loudspeakers in the drawing are producing identical sound waves. The waves spread out and overlap at the point P. This situation is analogous to Young’s double-slit experiment, except that sound waves are being used. What is the difference l 2 – l 1 in the two path lengths if point P is at the third sound intensity minimum from the central sound intensity maximum? Express this difference in terms of the wavelengths (  ) of the sound. 14. In certain Young’s double-slit experiment, an interference pattern is formed on a distant screen. The angle that locates a given bright fringe is small, so that the approximation sin  =  is valid. By what factor does the angle change if the wavelength (  ) is doubled and the slit separation (d) is doubled?

15. In a Young’s double-slit experiment the wavelength of light used is 461 nm (in vacuum), and the separation between the slits is 2.3x10 -6 m. Determine the angle that locates (a) the dark fringe for which m=0, (b) the bright fringe for which m=1, (c) the dark fringe for which m=1, and (d) the bright fringe for which m=2. 16. The dark fringe for m=0 in a Young’s double-slit experiment is located at angle of 15 degrees. What is the angle that locates the dark fringe for m=1?

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17. Two parallel slits are illuminated by light composed of two wavelengths. One wavelength is  A = 635 nm. The other wavelength is  B and is unknown. On a viewing screen, the light with wavelength  A = 635 nm produces its third-order bright fringe at the same place where the light with wavelength  B produces its fourth dak fringe. The fringes are counted relative to the central or zeroth-order bright fringe. What is the unknown wavelength? 18. In a Young’s double-slit experiment the separation distance (y) between the second- order bright fringe and the central bright fringe on a flat screen is 0.0150 m, when the light has a wavelength of 425 nm. Assume that the angles are small enough so that sin (  ) is approximately equal to tan (  ). Find the separation (y) when the light has a wavelength of 612 nm. 19. You are standing in air and are looking at a flat piece of glass (n=1.52) on which there is a layer of transparent plastic (n= 1.61). Light whose wavelength is 541 nm in vacuum is incident nearly perpendicularly on the coated glass and reflects into your eyes. The layer of plastic looks dark. Find the smallest possible nonzero value for the thickness of the layer.

20. When monochromatic light shines perpendicularly on a soap film (n= 1.33) with air on each side, the second smallest nonzero film thickness for which destructive interference of reflected light is observed is 442 nm. What is the vacuum wavelength of the light in nm? 21. A film of oil lies on wet pavement. The refractive index of the oil exceeds that of the water. The film has the minimum nonzero thickness such that it appears dark due to destructive interference when viewed in visible light with wavelength 680 nm in vacuum. Assuming that the visible spectrum extends from 380 to 750 nm, what is the longest visible wavelength (in vacuum) for which the film will appear bright due to constructive interference? 22. Monochromatic light (  vacuum = 625 nm) shines on a soap film (n= 1.33) that has air on either side of it. The light strikes the film perpendicularly. What is the minimum thickness of the film for which constructive interference causes it to look bright in reflected light?

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