Question

Light incident normally on a plane mirror attached to a galvanometer coil reflects backward as shown in figure. A current in the coil produces a deflection of $3.5^{\circ}$ of the mirror. The displacement of the reflected spot of light on a screen placed $1.0\, m$ away is

• A. $27.5\,m$
• B. $48.9\,m$
• C. $24.5\,m$
• D. $12.2\,m$

Answer 1

Answer: (C)

Angle of deflection is $\theta = 3.5^{\circ}$, Distance,
between the screen and the mirror is $= 2.0 \,m$
The reflected rays get deflected by an amount twice the angle of deflection,
i.e., $2\theta = 7.0^{\circ} $
$\therefore tan\, 2\theta = \frac{d}{2}$
$\Rightarrow d = 2 \times tan\,7^{\circ}$
$= 2 \times 0.1227$
$= 0.245\,m$
$ = 24.5\,cm$