Question

A beam of light from a source $L$ is incident normally on a plane mirror fixed at a certain distance $L$ from the source. The beam is reflected back as a spot on a scale placed just above the source $L$. When the mirror is rotated through a small angle $\theta$, the spot of the light is found to move through a distance y on the scale. The angle $\theta$ is given by

• A. $\frac{y}{2x}$
• B. $\frac{y}{x}$
• C. $\frac{x}{2y}$
• D. $\frac{x}{y}$

Answer 1

The correct option is B $\frac{y}{x}$

$\begin{array}{c}\text{The given optical situation}\\ \text{is depicted in following}\\ \text{figure :}\end{array}$

$\begin{array}{c}\text{when the mirror is rotated}\\ \text{by a small angle}\theta \text{, the}\\ \text{angle of refraction is}2\theta \text{.}\end{array}$

$\begin{array}{cc}\tan 2\theta & =\frac{y}{x}\\ \Rightarrow & 20=\frac{y}{x}\\ \Rightarrow & Q=\frac{y}{x}\\ & \therefore \theta =\frac{y}{x}\end{array}$ $\left[\begin{array}{cc}0& \text{is small.}\\ \text{so,}& \tan 2\theta =2\theta \end{array}\right]$