Question

Light incident normally on a plane mirror attached to a galvanometer coil retraces backwards as shown in Fig. A current in the coil produceds a deflection of `3.5^(@)` of the mirror. What is the displacement of the reflected spot of light on a screen placed 1.5 m away ?

Answer 1

Here, `theta=3.5^(@)`
`"x = 1.5m, d = ?"`
When the mirror turns through an angle `theta`, the reflected ray turns through double the angle.
`2theta=2xx3.5^(@)=7^(@)=(7pi)/(180)" rad"`
from figure,
`tan 2 theta=(SA)/(OS)=(d)/(1.5)xxd`
`=1.5xx(7pi)/(180)m=0.18m`
`d=1.5 tan 2 theta`
`~~1.5 (2theta)`
`=1.5xx(7pi)/(180)m=0.18m`