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 48.0 km due north. A detector is placed 132 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 0.0040°. By how many meters (due east) will the reflected ray miss the detector?

Explanation / Answer

As we know that

You have to draw a figure to solve the problem

tan = 132 m / 48000 m = 0.00275
= 0.157562996° = the angle made by the normal to the surface of the
mirror with due south

= + 0.0040° = 0.157562996° + 0.0040° = 0.161562996°

tan = opposite side opp / adjacent side adj

--> opp = adj tan
opp = ( 48000 m ) tan ( 0.161562996° ) = 135.3510582m

135.3510582 m - 132 m = 3.351058155 m

The reflected ray will miss the detector by a distance of 3.351058155 m

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