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 49.5 km due north. A detector is placed 124 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? degree (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 degree. By how many meters (due east) will the reflected ray miss the detector? m

Explanation / Answer

A)

thita = tan¹(124/49500) = 0.144 degrees

thita / 2 = 0.144 degrees / 2 = 0.072 degrees

B)

If this bearing is 0.005° too far east, then the reflected ray will have a bearing of
tan¹(124/49500)+2*0.005° east of south.
The reflected ray will cross the baseline joining the laser source and detector at a distance of
49500*tan(tan¹(124/49500)+0.01°) east of the source.
Calculate
49500*tan(tan¹(124/49500)+0.01°) = 133 m.
The ray will miss the detector by 133 - 124 = 9 m (eastward).

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