Question

An object is present on the principal axis of a concave mirror at a distance 30 cm from it. Focal length of mirror is 20 cm. If the object starts moving with $2cm{s}^{-1}$ along principal axis towards the mirror then :

• A. image starts moving with $4cm{s}^{-1}$ away from the mirror
• B. image starts moving with $4cm{s}^{-1}$ towards the mirror
• C. image starts moving with $8cm{s}^{-1}$ towards the mirror
• D. image starts moving with $8cm{s}^{-1}$ away from the mirror

Answer 1

The correct option is D image starts moving with $8cm{s}^{-1}$ away from the mirror

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

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

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

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

$\frac{\partial v}{\partial t}=\frac{\partial \left(\frac{fu}{u-f}\right)}{\partial t}$

$\frac{d_v}{d_t}=-\frac{f^2}{(u-f{)}^2}\times \frac{d_u}{dt}$

$=-\frac{{20}^2}{{10}^2}\times 2$

$=-4\times 2$

$=-8$(-ve sign indicates it is moving away from the mirror)

option $D$ is correct