A point source of light B is placed at a distance L in front of the centre of a mirror of width $' d'$ hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown in the figure. The greatest distance over which he can see the image of the light source in the mirror is [2000]

Question

Smart Achievers · Accepted Answer

(4)

The ray diagram is as follows:

From figure, $W X = P Q = d$

$Z S = R S = \frac{d}{2}$

$∵$ $P W = 2 P S$

$∴$ $V W = 2 R S = 2 (\frac{d}{2}) = d$

Similarly, $X Y = d$

$∴$ $V Y = V W + W X + X Y = d + d + d = 3 d$

Solution

1 $\frac{d}{2}$

2 $d$

3 $2 d$

4 $3 d$

Ans.
(4)

The ray diagram is as follows:

From figure, $W X = P Q = d$

$Z S = R S = \frac{d}{2}$

$∵$ $P W = 2 P S$

$∴$ $V W = 2 R S = 2 (\frac{d}{2}) = d$

Similarly, $X Y = d$

$∴$ $V Y = V W + W X + X Y = d + d + d = 3 d$

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Solution

1 d2

2 d

3 2d

4 3d