An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be

Options

A. 30 cm towards the mirror
B. 36 cm away from the mirror
C. 30 cm away from the mirror
D. 36 cm towards from the mirror .

Answer

B

Explanation

`(1)/(f)=(1)/(v_(1))+(1)/(u)`
`-(1)/(15)=(1)/(v_(1))-(1)/(40)`
`implies (1)/(v_(1))=(1)/(-15)+(1)/(40)`
`v_(1)` =-24 cm
When object is displaced by 20 cm towards mirror
`u_(2)=-20`
`(1)/(f)=(1)/(v_(2))+(1)/(u_(2))`
`(1)/(-15)=(1)/(v_(2))-(1)/(20)`
`(1)/(v_(2))=(1)/(20)-(1)/(15)`
So, image shifts away from mirror by `=60-24=36 cm`