Physics 8: Homework 8 Additional Questions


In addition to the problems from the book (14.E.3, 14.E.8, 14.E.10, 14.E.11, 14.E.12), here are more problems that are a required part of the assignment:

  1. A retro-reflector, or corner-cube, returns light back in the same direction from which it came. These are used in bike reflectors, for instance. A two-dimensional corner-cube is drawn below, consisting of two mirrors at right angles. Complete the drawing of the ray path. Note in your answer how the final ray direction compares to the initial (drawn) ray direction. If you're ambitious (not required), you can convince yourself that this property holds no matter what the direction of the incoming ray (other than just horizontal, as shown).
  2. Can a fish see clearly when it jumps out of the water? Why or why not?
  3. Episode II: Attack of the Angler In a pond far, far away, a technologically advanced fisherman—let's call him Fishbacca—takes aim at a fish a few feet underwater with his laser gun. Should Fishbacca aim high, low, or right at the image of the fish? Explain why and draw a picture.
  4. Episode III: Revenge of the Fish Unfortunately for Fishbacca, this is no ordinary fish, but Darth Ictheous, whose signature weapon is a formidable spear. Fishbacca fails to hit Darth Ictheous (either the sinister fish evaded the laser blast or Fishbacca misunderstood the physics of refraction), and now prepares to hurl his spear back at Fishbacca, who is standing on the bank of the pond. Should Darth Ictheous aim high, low, or right at the image of Fishbacca? Explain why and draw a picture.
  5. When light hits a surface where the refractive index changes, some of the light is transmitted and some is reflected. The formula for reflection is: R = [(n2 - n1)/(n2 + n1)]2. Calculate the amount of reflection at the following interfaces, using the fact that the refractive indices of air, water, glass, and diamond are 1.00, 1.33, 1.52, and 2.42, respectively. Express your answers as percent reflection.
    1. air - water
    2. air - glass
    3. water - glass
    4. air - diamond
    Note that this quantitatively explains why raindrops on the sidewalk look dark: the air-sidewalk interface (much like air-glass, refractively) is roughly ten times more reflective than the water-sidewalk interface.
  6. Explain why ice without air bubbles is clear, but ice riddled with lots of tiny air bubbles looks white.
  7. Given what you know about why the sky is blue, explain why the sun looks slightly yellow-ish, and why as the sun sets it gets more orange and perhaps even red. A relevant question to ask yourself: how much air do the rays from the sun have to traverse?
  8. In principle, if your eyes were sensitive enough, could you see a moonbow—a rainbow with the moon rather than the sun as a source? In which direction (relative to the moon) would you have to look?

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