Question

A point object ${}^{\prime }{O}^{\prime }$ is at the center of curvature of a concave mirror. The mirror starts to move at a speed $u$, in a direction perpendicular to the principal axis. Then, the initial velocity of the image is

• A. $2u$, in the direction opposite to that of mirror's velocity
• B. $2u$, in the direction same as that of mirror's velocity
• C. Zero
• D. $u$, in the direction same as that of mirror's velocity

Answer 1

The correct option is B $2u$, in the direction same as that of mirror's velocity

$u=-2f$ ; $f=-f$

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$

$\frac{1}{v}+\frac{-1}{2f}=\frac{-1}{f}$

$v=\frac{fu}{f-u}=-2f$

magnification is $-\frac{v}{u}=-\frac{2f}{2f}=-1$

wrt mirror the object moves with a speed $u$ opposite to direction of mirror

speed of image is $magnification\times u$

$=-1\times u$

$=-u$ (-ve sign indicates direction is in that of mirror)

but mirror is also moving with a speed u hence total speed of image is

$u+u=2u$ in the direction of mirror velocity

option $B$ is correct