In an experiment designed to measure the speed of light, a laser is aimed at a m

Question

In an experiment designed to measure the speed of light, a laser is aimed at a mirror that is 50.0 km due north. A detector is placed 140 m due east of the laser. The mirror is to be aligned so that light from the laser refelects 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 0.0020°. By how many meters (due east) will the reflected ray miss the detector?

Explanation / Answer

part A:

angle due to south

tan phi = (LD)/LM

phi =1/2 tan^-1(140 /50000)

phi = 0.08 deg

-------------------------

D1D2 = LD2 - LD1

LM *(LD1/LM) + tna 2 theta /(1- LD/LM tan 2thea - LD1

D1D2 = 50000* ((140/50000 + tan (2 * 0.002))/(1-(140/50000 tan (2* 0.003)) - 140

D1D2 = 3.49 m

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