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course Phy 202
3/14 2pm 3.2.11
`q001. Light parallel to the axis of a thin lens is focused at distance f from the lens. A parallel beam originates at the tip of a candle at distance o from the lens and is refracted through the focal point. Another beam originates from the same point, strikes the lens at its center and passes through the lens undeflected.
At what distance i from the lens do the two rays meet? Answer by sketching the rays, forming a series of similar triangles and solving the resulting proportionalities.
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As discussed in class, 1/I +1/o= 1/f
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`q002. The image of an object originally at distance o from a lens with focal length f forms at distance i from the lens, where 1 / i = 1 / f + 1 / o.
If f = 10 cm, at what distance from the lens will the image of an overhead light 120 cm above the lens be formed?
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1/10 cm =1/i +1/120 cm
1/i = 1/ .092 cm=10.9 cm
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If another lens of equal focal length is placed 20 cm below that image, it will form an image of the image. How far below the lens will the image of the image form?
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1/20 cm=1/i + 1/140 cm
1/i= 1/.043 cm=23.3 cm
@& The object for this lens is the image formed by the first lens, not the light itself. f is the focal length of the lens, which is 10 cm, not 20 cm. The lens is placed 20 cm below the image formed by the first lens, so for this lens the object distance is 20 cm.*@
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Is it possible to form an image of the first image on a tabletop 180 cm below the lens? If not, show why not. If so, show how far below the first image the lens must be placed.
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1/f=1/180 cm+1/120 cm
1/f=1/.013 cm= 72 cm
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Challenge question: Two lenses of focal lengths f_1 and f_2 are to be used to form an image of an overhead light, with the image being formed on a screen at distance s from the light. If the first lens is held at distance s_1 below the light, then for what values of s_1 is it possible, using the second lens, to form on the screen an image of the first image? In terms of s_1, what is the distance s_2 of the second lens from the light?
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`q003. Light of wavelength 600 nm strikes a thin film of oil on top of a layer of water. Some of the light reflects off the surface of the film, and some off the surface of the water.
If the thickness of the film is 450 nm, will the two reflected beams interfere positively, negatively, or somewhere in between?
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Will interfere out of phase or negatively as it will be the equivalent of 1.5 wavelengths
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Give three film thicknesses that will cause positive interference, and three that will cause negative interference.
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300 nm, 600 nm 900 nm
Negative—750 nm 1050 nm 1350 nm.
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The wavelength of the light as is passes through the oil is in fact less than the 600 nm wavelength. If the index of refraction of air is very close to 1 and the index of refraction of the oil is 1.5, then how does this affect your results?
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`q004. A long line of elephants, trunk to tail, is passing you. The elephants move at a steady speed of 2 meters / second, and each elephant is 5 meters long. Your job is to smile in greeting to every elephant that passes you. With what frequency do you have to smile?
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Have to smile .4 smiles/second
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If you walk at .5 meter / second in the direction opposite that of the elephants, with what frequency will you need to smile?
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Have to smile .5 smiles/second
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If you back up at .5 meter / second, with what frequency will you need to smile?
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Have to smile .3 smiles/second
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If the elephants are on a moving walkway, which is moving at .5 meter / second in your direction, with you standing, with what frequency will you need to smile?
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Each elephant will pass in 2.5 seconds. Smile every 2.5 seconds, the equivalent of .35 smiles/second
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`q005. The speed of sound in aluminum is about 6400 m/s. The aluminum rod we used was about 108 cm long. I held the rod in the middle, creating a node at that point. The ends of the rod were free to vibrate so there are antinodes at the ends. What therefore was the frequency of the sound created in that rod?
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The wavelength is about 216 cm long. The speed is 6400 m/s, therefore frequency is
6400 m/s/2.16 m=2962.9 cycles/s
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`q006. When I threw the 'singing rod' at you, at the instant it left my hand it was about 15 meters away. The first 'peak' of the sound wave that left the end of the rod after I released it was 15 meters from you and hadn't yet reached your ear.
Moving at 340 m/s, how long did it take that first peak to get to your ear?
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15 m/340 m/s=.044 s
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The rod didn't hit you in the ear. I threw it so that it would land a few meters in front of you, so as to avoid damaging the rod (or you). Suppose that there was a microphone at the point where the rod hit, so that the rod actually hit the microphone at a distance 12 meters from where I released it, and suppose that you were listening to the signal from the microphone
You will agree that in traveling that 12 meters the rod emitted a number of peaks. How long did it take the rod to get to that point, and how many peaks were produced, if we assume that the frequency of the sound produced is 2500 Hz?
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F=2500hz, Wavelength is 2.16 m so c=2500Hz*2.16 m=5400 m/s
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How long did it take first peak to reach the microphone?
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12 m/340 m/s= .035 seconds
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Assuming that the rod traveled at 20 meters / second, how long did it take the rod to reach the microphone?
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20 m/s / 12 m=1.67 s
@& At 20 m/s, it will take less than a second to travel 12 m.
Also, m/s / m = s^-1, not s.*@
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From the time the first peak reached the microphone, until the rod hit the microphone, how much time elapsed?
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1.67 s- .035 s=1.635 s
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How many peaks were therefore detected by the microphone, and during what time interval were they detected?
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340 m/s/1.635 s=208 peaks
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What therefore was the frequency detected by the microphone?
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f=speed/wavelength=340 m/s / 208 = 1.6
I know this probably isn’t completely right, but I’m confused as to what else to do to for it.
@& The questions are a little out of order. You needed the 20 m/s speed before you were given that information.
It takes .6 sec for the rod to reach the microphone, during which you have 2500 cycles / sec * .6 sec = 1500 cycles.
They are received in .6 sec - .035 sec.
From this you can calculate the frequency detected by the microphone.*@
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`q007. Suppose that rather than me throwing the rod at you, you threw the microphone at the rod at 20 m/s, while I held it stationary. Use an analysis similar to the one above to find the frequency that would be detected by the microphone. Your answer will be close to, but not identical with, the answer you got above.
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`q008. If there was a microphone stationary at the rod, and its signal was mixed with the signal from the microphone you threw, how many beats per second would be observed?
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`q009. From the measurements you made in Monday's class, what do you get for the wavelength of laser light?
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I know it’s been quite awhile since then, but I don’t believe we physically measured anything with the laser light.
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@& You measured the distance between the bright spots on the screen.*@
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