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A point objec...

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 $2 d$ from the mirror. The range of distance over which the observer can see the image of the object in the mirror is

A

L

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B

3 L

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C

2 L

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D

\frac{L}{2}

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Solution

The correct option is B $3 L$

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

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

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

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

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

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