A laser is aimed at a mirror that is 50.0 km due north. A detector is placed 117

Question

A laser is aimed at a mirror that is 50.0 km due north. A detector is placed 117 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? b) Suppose the mirror is misaligned, so that the actual angle between the normal to the surface and due south is too large by 0.004 degrees. By how many meters (due east) will the reflected ray miss the detector?

Explanation / Answer

tan theta = 117/50000 theta = .134 deg angle detector makes with North a) Angle of normal to mirror = theta / 2 = .067 deg b) If angle of normal (with S) = .067 + .004 = .071 then theta = 2 * .071 = .142 tan theta = D / 50000 D = 124 m Reflected ray will miss by 7 m

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