Question

A plane mirror of length $8\text{cm}$ is moving with a speed of $3\text{m/s}$ towards a wall as shown in the figure. The diametrical length of spot formed on the wall is?
(Assume spot to be circular)

• A. $4\text{cm}$
• B. $16\text{cm}$
• C. $8\text{cm}$
• D. $24\text{cm}$

Answer 1

The correct option is B $16\text{cm}$


As shown in the figure, from geometry we have
Diametrical length of spot formed $=\text{AC}-\text{AB}$
Here, by applying similar triangle property we get $AC=(16+x)$
So we have diametrical length as
$=(16+x)-x$
$=16\text{cm}$

Alternate:
In such cases, diametrical length of spot $=2\times \text{length of mirror}$
$=2\times 8=16\text{cm}$

Key point: Size of spot is independent of speed of mirror, position of source on the wall and distance of mirror from the spot.