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 58.0 km due north. A detector is placed 101 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

Given,

let be the angle between the incident and reflected rays

tan = 101 /58000

=> = tan-1(101 /58000) = 0.099°

since incident angle = reflected angle and incident angle + reflected angle =

the asked angle = angle of incidence, = /2 = 0.0498°

b) now incident angle, = 0.0498 + 0.0040 = 0.0538°

therefore, = 2 = 0.1076

let the new detector position be x meter due east from source

tan = x/58000 = 1.878 x 10-3

So, x = 108.92 m

therefore shift in detector positon = x - 101= 7.923 m away from source due east

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