Question

In an experiment designed to measure the speed of light, a laser is aimed at a mirror that is 52.0 km due north. A detector is placed 107 m due east of the laser. The mirror is to be aligned so that light from the laser reflects into the detector.

(a) When properly aligned, what angle should the normal to the surface of the mirror make with due south?

(b) Suppose the mirror is misaligned, so that the actual angle between the normal to the surface and due south is too large by 0.005

Answer 1

a)
      let @ be the angle between the incident and refllected rays.
      So,
         tan@ = 107 m/52000 m
              ? = 0.118 degree
      Since, incident angle = reflected angle
      And
     incident angle + reflected angle = @
      Therefore, the required angle is given by
            ? = @/2
               = 0.0589 degrees
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b)
      Now incident angle, ?' = 0.0589o + 0.005o
                                           = 0.06395 degrees
      Therefore, angle @' = 2?'
                                    = 0.1279 degrees

      Let the new detector position be x meter due east from source,
                            tan@' = x/52000 m
                                   x = (52000 m)(tan0.1279)
                                      = 116.08 m
      Therefore shift in detector positon = x - 107 m
                                                            = 9.08 m away from source due east