Question

Light incident normally on a plane mirror attached to a galvanometer coil retraces backwards as shown in Fig. 9.36. A current in the coil produces 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

given, deflection produced of the mirror due to current in the coil, $\theta$ = 3.5°

so, the reflected light deflect by $2\theta$ =2(3.5°) = 7°.

distance between reflected spot of light and screen , D = 1.5m

deflection of the spot d can be calculated as $tan2\theta=\frac{d}{D}$

or, tan7° = d/1.5

or, d = (1.5)tan7° = 1.5(0.1228)

or, d = 0.1842 m or 18.42 cm

hence, displacement of the reflected spot of light is 18.42cm.

Answer 2

Given:

Angle of deflection, θ = 3.5°

Distance of the screen from the mirror, D = 1.5 m

The reflected rays get deflected by an amount twice the angle of deflection i.e.,

2θ = 7.0°

The displacement (d) of the reflected spot of light on the screen is given as:

tan2θ = d/1.5

(Using trigonometric ratio)

d = 1.5 x tan7o

d= 0.184 m = 18.4 cm

Hence, the displacement of the reflected spot of light is 18.4 cm.