Question

An object is placed at a distance of 40cm from a concave mirror of focal length 15cm. If the object is displaced through a distance of 20 cm towards the mirror, By how much distance is the image displaced??.

Answer 1

It just needs to be done as two separate calculations then the difference of the two answers is found.

In the initial setup, the object distance is 40 cm, which gives 24 cm image distance given the focal length of 15 cm. (equation: 1/15= 1/40 + 1/i)

The second equation changes object distance to 20 cm (40–20), which results in 60 cm as the image distance. (equation: 1/15= 1/20 + 1/i)

The difference between 60 and 24 is 36 cm (in the direction away from mirror).

Answer 2

GIVEN:-
u=-40cm
f=-15cm
u'=-20cm

first 1/f=1/u+1/v
1/v=1/f-1/u
=-1/15+1/40
= -1/24
*** v=-24cm
Again
1/f'=1/u'+1/v'
1/v'=1/f'-1/u'
=-1/15+1/20
= -1/60
***** v' = -60 cm
the image is displaced is 20cm