Physics 112 HW29
due Thursday, 17 December 2015
EMI06. White light reflects at normal incidence from the top and bottom surface of a glass plate (n = 1.52). There is air above and below the plate. Constructive interference is observed for light whose wavelength in air is 477.0 nm. What is the thickness of the plate if the next longer wavelength for which there is constructive interference is 540.6 nm?
EMI07. An oil tanker spills a large amount of oil (n = 1.45) into the sea (n = 1.33). If you look down onto the oil spill from overhead, what predominant wavelength of light do you see at a point where the oil is 380 nm thick? What color is the light?
D01. Monochromatic light from a distant source is incident on a single slit 0.750 mm wide. On a screen 2.00 m away, the distance from the central maximum of the diffraction pattern to the first minimum is measured to be 1.35 mm. Calculate the wavelength of the light.
D02. High-frequency sound from a distant source with wavelength 9.00 cm passes through a narrow slit 12.0 cm wide. A microphone is placed 40.0 cm directly in front of the center of the slit, corresponding to point O in the diagram. The microphone is then moved in a direction perpendicular to the line from the center of the slit to point O. At what distances from O will the intensity detected by the microphone be zero?
R01. You are asked to design a space telescope for Earth orbit. When Jupiter is 5.93 ´ 108 km away (its closest approach to Earth), the telescope is to resolve, by Rayleigh’s criterion, features on Jupiter that are 250 km apart. What minimum diameter mirror is required? Assume a wavelength of 500 nm.
R02. The Hubble Space Telescope has an aperture of 2.4 m and focuses visible light (400 nm to 700 nm). The Arecibo radio telescope in Puerto Rico is 305 m (1000 ft) in diameter (it is built in a mountain valley) and focuses radio waves of wavelength 75 cm.
a) Under optimal viewing conditions, what is the smallest crater that each of these telescopes could resolve on our moon?
b) If the Hubble telescope were to be converted to surveillance use, what is the highest orbit above the surface of the Earth if could have and still be able to resolve the license plate (not the letters, just the plate) of a car on the ground? Assume optimal viewing conditions so that the resolution is diffraction limited.
DI01. In class we did an example of a two-slit interference/diffraction pattern where the ratio d/a = 4. There were 7 bright interference spots within the broad diffraction envelope at the center of the pattern.
a) What must the ratio d/a be if the broad central diffraction envelope contains exactly 5 bright interference spots?
b) In the case in part (a), how many interference bright spots are contained within the first broad diffraction maximum on either side of the central one?
DI02. An interference pattern is produced by monochromatic light of wavelength 630 nm from a distant source incident on two identical, parallel slits separated by a distance (between centers) of 0.840 mm.
a) It is found that the m = 3 interference maximum is missing from the pattern because it coincides with the first diffraction minimum. What is the width of each slit?
b) Which other interference maxima should also be missing from the pattern?
c) If the wavelength is decreased from 630 nm to 420 nm, which interference maxima will be missing from the pattern?
DI03. If a diffraction grating produces its third-order (m = 3) bright spot at an angle of 78.4o for light of wavelength 681 nm, find
a) the number of slits per centimeter for the grating;
b) the angular location of the first-order and second-order bright spots.
c) Will there be a fourth-order bright spot? Explain.
(over)