5. Assume the indices of refraction for air, water, andglass are 1.00, 1.33, and 1.50, respectively. Whenilluminated from above, a ray reflected from theair-water interface undergoes a phase shift of o, =T, and a ray reflected at the water-glass interfacealso undergoes a phase shift of n. Thus, the tworays are unshifted in phase relative to cach otherdue to reflection. For constructive interference, thepath difference 2t must equal an integer number(m) of wavelengths in water.air14%=(2/2)27+xwaterglassa. Derive the equation in terms of A based on the situation above.b. If this m-value is an integer the wavelength undergoes constructive interferenceupon reflection in terms of A, compute for the wavelengths for the followingthickness: t- 2 x 10°m at mr00 nm and m.o0 am

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Answered: 5. Assume the indices of refraction for…

University Physics Volume 3

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Chapter3: Interference

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Problem 91CP: A film of oil on water will appear dark when it is very thin, because the path length difference...

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In Section 9.6, we described how the speed of light varies with wavelength (or frequency) for transparent solids. But the speed of light in matter is also a function of temperature and pressure. This dependence is most marked for gases and is instrumental in producing such things as mirages and atmospheric refraction, the latter phenomenon being the displacement of an astronomical object (like the Sun or another star) from its true position because of the passage of its light through the atmosphere. Because Earth’s atmosphere is a gaseous mixture and easily compressed, its density is highest near Earth’s surface and gradually declines with altitude. (Refer to the discussion in Section 4.4 and Figure 4.29.) Thus, the speed of light in the atmosphere is lowest near the surface and gradually gets higher, approaching c as one goes farther and farther into space. Using this fact and the law of refraction, sketch the path a light ray from the Sun would follow upon entering Earth’s atmosphere, and predict the apparent position of the Sun relative to its true position (Figure 9.85). What does this tell you about the actual location of the Sun’s disk relative to your local horizon when you see it apparently setting brilliantly in the west in the evening?
Is it possible that total internal reflection plays a role in rainbows? Explain in terms of indices of refraction and angles, perhaps referring to Figure 25.48. Some of us have seen the formation of a double rainbow. Is it physically possible to observe a triple rainbow? Figure 25.48 Double rainbows are not a very common observance. (credit: InvictusOU812, Flickr)
Referring to the electric room heater considered in the first example in this section, calculate the intensity of IR radiation in W/m2 projected by the concave mirror on a person 3.00 m away. Assume that the healing element radiates 1500 W and has an area of 100 cm2, and that half of the radiated power is reflected and focused by the mirror.
Suppose you are using total internal reflection to make an efficient corner reflector. If there is air outside and the incident angle is 45.0°, what must be the minimum index of refraction of the material from which the reflector is made?
If b is Brewster's angle for light reflected from the top of an interface between two substances, and b is Brewster's angle for light reflected from below, prove that b+b=90.0.
Consider a common mirage formed by superheated air immediately above a roadway. A truck driver whose eyes are 2.00 m above the road, where n = 1.000 293, looks forward. She perceives the illusion of a patch of water ahead on the road. The road appears wet only beyond a point on the road at which her line of sight makes an angle of 1.20 below the horizontal. Find the index of refraction of the air immediately above the road surface.
A fish looks up toward the surface of a pond and sees the entire panorama of clouds, sky birds, and so on, contained in a narrow cone of light, beyond which there is darkness. What is going on here to produce this vision, and how large is the opening angle of the cone of Light received by the fish?
A cataract is cloudiness in the lens of the eye. Is light dispersed or diffused by it?
What is the speed of light in air? In crown glass?
What happens to a light wave when it travels from air into glass? (a) Its speed remains the same. (b) Its speed increases. (c) Its wavelength increases. (d) Its wavelength remains the same. (e) Its frequency remains the same.
What are the three smallest non-zero thicknesses of soapy water (n=1.33) on Plexiglas if it appears green (constructively reflecting 520-nm light) when illuminated perpendicularly by white light?
The index of refraction for crown glass is 1.512 at a wavelength of 660 nm (red), whereas its index of refraction is 1.530 at a wavelength of 410 nm (violet). If both wavelengths are incident on a slab of crown glass at the same angle of incidence, 60.0, what is the angle of refraction for each wavelength?

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