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 50.0 km due east and have it detected by a light sensor that is 117 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.
_____ m

Explanation / Answer

According to the setup

a) Let the angle between incident ray and the reflected ray from the mirror = a

tan ( a) = 117 / 50000 =0.00234

So angle a = 0.134 °

Since by law of reflection

Angle of incidence equals angle of reflection and

Incident ray travels due east

The angle made by normal to the mirror with due west = a / 2

= 0.134 / 2 = 0.067°

b) since the actual angle between normal to mirror and due West is more by = 0.004°

The angle between incident ray and reflected ray will be more by = 0. 004 × 2 = 0.008 °

So actual angle a ( x) = 0.134° + 0.008 =0.142°

tan ( x ) = 0.00248

The actual distance of sensor due south

is = 124 m

Distance by which it need to be moved =

= 124 -117 = 7 m

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