For an independent study project, you design an experiment to measure the speed

Question

For an independent study project, you design an experiment to measure the speed of light. You propose to bounce laser light off a mirror that is 54.5 km due east and have it detected by a light sensor that is 111 m due south of the laser. The first problem is to orient the mirror so that the laser light reflects off the mirror and into the light sensor.

(a) Determine the angle that the normal to the mirror should make with respect to due west.

(b) Since you can read your protractor only so accurately, the mirror is slightly misaligned and the actual angle between the normal to the mirror and due west exceeds the desired amount by 0.004°. Determine how far south you need to move the light sensor in order to detect the reflected laser light.

Explanation / Answer

(a) tan(angle) = 111/(54.5*103)
angle = 0.11669 degrees
(b) if angle exceeds by the 0.004 then the angle becomes
0.11669+0.004 = 0.12069
therfore
tan0.12069 = South distance /(54.5*103)
south distance = 114.8 m
Hence the light sensor should be move by = 114.8 - 111 = 3.8 m

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