Question

In an experiment designed to measure the speed of light, a laser is aimed at a mirror that is 47.5 km due north. A detector is placed 116 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 0.005

Answer 1

The following figure shows the alingment of experiment:

            

(a) Let θ be the angle between the incident and refllected rays from the mirror.

From the figure use trignometry to find the angle.

thus, angle

From the figure this angle is equal to incident angle + reflected angle.

From laws of reflection: incident angle = reflected angle

Thus, the angle should the normal to the surface of the mirror make with due south

angle of incidence, i = r = θ/2 = 0.0699^o

(b)

When the incident angle, i = 0.0699 + 0.0050 = 0.0749^o

thus, the angle θ = 2*i = 0.1498^o

Let the detector position be x meter due east from source.

Again from the figure:

     

              0.0026145 = x/47500 m

              x = 124

   Therefore, the shift in detector positon is

          away from source due east.