Question

A point object is placed in front of a plane mirror, at distance $d$ from the centre of the mirror of width $L$ as shown in the figure. An observer is moving on a straight line on the same side of the mirror, parallel to it at a distance $2d$ from the mirror. The range of distance over which the observer can see the image of the object in the mirror is

• A. $L$
• B. $3L$
• C. $2L$
• D. $\frac{L}{2}$

Answer 1

The correct option is B $3L$


Let the range of distance over which the observer can see the image of the object be $2y$.

From the figure, $△PQR$ and $△P^{\prime }Q{R}^{\prime }$ are similar triangles. So, we can say that

$\frac{\frac{L}{2}}{y}=\frac{d}{3d}\Rightarrow y=\frac{3L}{2}$

Therefore, total range of distance for which the image is visible is given by

$2y=2\times \frac{3L}{2}=3L$