Question

An object is placed at a distance of `40 cm` from a concave mirrorr of focal length `15 cm`. If the object is displaced through a distance of `20 cm` towards the mirrorr, the displacement of the image will be
A. 30 cm towards the mirror
B. 36 cm away from the mirror
C. 30 cm away from the mirror
D. 36 cm towards the mirror

Answer 1

Correct Answer - B
Key concept The net displacement of the images is equal to the difference between the image distances in both the cases.
case 1 When the object distance, `u_(1) = -40cm`
Focal length of mirror, `f=-15cm`

Using the mirror formula, we get
`1/f = 1/v_(1) +1/u_(1)`
Substituting the given values, we get
`-1/15 = 1/v_(1)+ (-1/40)`
`rArr 1/v_(1) = 1/40 -1/15 = (3-8)/(120)=-5/120)`
`rArr v_(1)= (-120)/5 = -24cm`
Case 2 When the object distance, `u_(2)=20cm`

using the mirror formula, we get
`1/f = 1/v_(2)+1/u_(2)`
substituting the given values, we get
`-1/15 = 1/v_(2) + (-1/20)`
`rArr 1/v_(2)=1/20-1/15=(3-4)/60 = -1/60`
`rArr v_(2) = -60cm`
`therefore` The displacement of the image is
`=v_(2)-v_(1) = -60-(-24)=-60+24`
or `=-36 cm`
= 36 cm, away from the mirror