Question

An object is moving towards a concave mirror of focal length 24 cm.when it is at a distance of 60 cm from the mirror its speed is 18 cm/s.the speed of its image at that insrant is:(a)4 cm/s towards the mirror (b)8 cm/s towards the mirror (c)4 cm/s away from the mirror (d)8 cm/s away from the mirror

Answer 1

8 cm Towards the mirror

Answer 2

Answer:

we have

$\frac{1}{f} =\frac{1}{u} +\frac{1}{v} .........(1)\\\\or,\frac{1}{-24} =\frac{1}{-60} +\frac{1}{v} \\v=40\\v/u=40/60=2/3$

Differenciating equation (1) with respect to time

$0=\frac{-1}{u^{2} } \frac{du}{dt} -(\frac{-1}{v^{2} })\frac{dv}{dt}$

or,$0=\frac{-1}{u^{2} } v_{obj} -(\frac{-1}{v^{2} })v_{img}$

or, $v_{img}=-(\frac{v^{2} }{u^{2} } )v_{obj$

            =-(2/3)²*18

          =-8cm/s

=8cm/sec