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College Physics Problems

1. 10 nanometer x-rays are incident on a cubic crystal. A first order bragg diffraction maximum is observed when the incident beam makes an angle of 40 degrees with respect to the surface of the crystal. What is the spacing between the crystal planes?

2. The spacing between adjacent atomic planes in a crystal is 12 nanometers. An x-ray beam of wavelength 6 nanometers is incident upon the surface of the crystal.
a) What is the smallest incident angle (with respect the horizontal) which will result in a bragg diffraction maximum.
b) How many angles will result in a Bragg maximum, and what are they?
c) What is the frequency of the x-ray beam?

3. White light in air is incident of a piece of glass, which acts as a reflecting surface. The index of refraction of the glass is 1.5. At what incident angle will the reflected light be completely polarized.

4. Using a polarizer, it is observed that white light, passing through air, is completely polarized after reflecting off a surface at an angle of 57^o. What is the index of refraction of the reflecting material?

5. An unpolarized light beam is incident on two polarizers, as shown in the diagram below. The axis of polarization of the first polarizer makes an angle of 30 degrees with the horizontal. The axis of polarization of the second polarizer makes an angle of 60 degrees with the horizontal. If the incident intensity of the light is 100 watts/m², what is the intensity of the light after passing through the two polarizers?

6. If the electric field amplitude of the incident light beam in problem #5 were 100 newtons/coulomb, what would be the amplitude of the beam after passing through the two polarizers?

7. An astronaut in orbit is using a six diameter inch reflecting telescope to observe two mountains on the moon. The astronaut is 3.8 x 10⁵ km from the moon, and is observing the mountains in the 540nm wavelength region. The mountains are so close that they can just be resolved as being two separate objects. How far are the mountains apart?

8. Two bright lights are separated by a distance of 100 meters. A student starts to back away from the lights. Assuming the pupil of the eye has a diameter of two centimeters, how far can the student be from the lights and still distinguish them as separate objects? Use light of wavelength = 560 nm. (The answer to this is not realistic due to scattering and dispersion effects of the atmosphere.)