Homework #10 complete by Wednesday, March 9

1. Two slits are separated by 0.320 mm. A beam of 500-nm light strikes the slits, producing an interference pattern. Determine the number of maxima observed in the angular range -30 degrees to +30 degrees on the screen.

2. A possible means for making an airplane invisible to radar is to coat the plane with an antireflective polymer. If radar waves have a wavelength of 3.00 cm and the index of refraction of the polymer is n=1.50, how thick would you make the coating?

3. A screen is placed 50.0 cm from a single slit, which is illuminated with 690-nm light. If the distance between the 1st and 3rd minimae in the diffraction pattern is 3.00mm, what is the width of the slit?

4. You observe that a light source shown through a diffraction grating of 3660 slits per cm produces three discrete 1st order spectral lines at angles in degrees of 10.09, 13.71, and 14.77.
(a) What are the wavelengths of the light?
(b) At what angles are these lines found in the 2nd order spectrum?

5. If we were to send a ruby laser beam (wavelength of 694.3 nm) outward from the barrel of a 2.70-m-diameter telescope, what would be the diameter of the big red spot when the beam hit the Moon 3.84 x 10⁵km away?

6. Assume the range of pupil variation during adaptation of a normal eye is from 2 to 7 mm. What is the corresponding range of distances over which the eye can detect the separation of objects 1 in. apart?

7. The Very Large Array (VLA) is a set of 27 radio telescope dishes in New Mexico. Each dish is 25 meters in diameter. The antennae can be moved apart on railroad tracks, and their combined signals give the resolving power of a synthetic aperture 36.0 km in diameter.

(a) If the detectors are tuned to a frequency of 1.4 x 10⁹ Hz, what is the angular resolution of one of the dishes? Of the array of dishes? Convert your answers from radians to arcsec (1 degree = 60 arcminutes = 3600 arcseconds).
(b) Clouds of hydrogen radiate at this frequency. What must be the separation of two clouds at the center of the galaxy (26,000 lightyears = 2.5 x 10²⁰ m) if they are to be resolved?
(c) Very Long Baseline Interferometry (VLBI) is a method of using telescopes spread across the Earth's surface to observe objects at high resolution. Part of this network is located across the United States. See this link for a map of sites. Called the Very Long Baseline Array ( VLBA) , it consists of 10 telescopes of 25-m-diameter. Such a network allows angular resolutions of better than a milli-arcsecond. Using this resolution, what is the minimum separation of two clouds at the center of the galaxy for them to be resolved by the VLBA?
(d) The VLBA homepage claims that this resolution is equivalent to being able to read a newspaper in New York from the distance of Los Angeles. Check this claim.

8. Three polarizing disks are centered on a common axis and held parallel to each other. The transmission axes of the disks have the following angles measured from the vertical direction: q₁ = 20.0, q₂ = 40.0, q₃ = 60.0. A plane-polarized beam of light with E₀ parallel to the vertical direction is incident from the left on the first disk with a flux density I₀ = 10.0 units. Calculate the transmitted flux density I_f.

9. How far above the horizon is the Moon when its image reflected in calm water is completely polarized? (n_water = 1.33)

    Problems extracted from Haliday, Resnick, & Walker, Serway & Beichner, Pedrotti & Pedrotti

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Last updated March 6, 2005