Question

An object is moving with the velocity 40 cm towards the concave mirror. The position of object is 10 cm from
the mirror. If object is moving along the principal axis, then find the velocity of image (focal length of mirror is
30 cm)​

Answer 1

Given that,

Focal length f=24cm

Distance from the mirroru=60cm

Now, by using mirror formula

f

1

​

=

v

1

​

+

u

1

​

......(I)

24

1

​

=

v

1

​

+

60

1

​

v

1

= 401

v=40cm

Now, on differentiating of equation (I) f1​

= v1 + uu1 0=− v 21dtdv​ − u 21dtdudtdv​

= u 2 −v 2dtdudtdv

​ = 60×60−40×40 ×9dtdd=−4cm/s

Negative sign indicate that the velocity of the image is away from the mirror

Hence, the velocity of the image is 4 cm/s