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 object starts moving with $2cm{s}^{-1}$ perpendicular to principal axis above axis then :

• A. image moves with velocity $4cm{s}^{-1}$ below the principal axis
• B. image moves with velocity $4cm{s}^{-1}$ above the principal axis
• C. image moves with velocity $8cm{s}^{-1}$ below the principal axis
• D. image moves with velocity $8cm{s}^{-1}$ above the principal axis

Answer 1

The correct option is A image moves with velocity $4cm{s}^{-1}$ below the principal axis

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

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

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

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

Magnification is $-\frac{v}{u}=\frac{f}{f-u}$

Velocity of image $=\frac{\partial \left(heightofobject\right)}{\partial t}\times \frac{f}{f-u}$

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

$=-4(<0)$ i.e, moving downwards