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

Options

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

Answer

B

Explanation

Using mirror formula,
`(1)/(f)=(1)/(v_(1))+(1)/(u),-(1)/n(15)=(1)/(v_(1))-(1)/(40)implies(1)/(v_(1))=(1)/(-15)+(1)/(40)`
`v_(1)=-24cm`
When object is displaced by `20` cm towards mirror. Now, `u_(2)=-20cm`
`(1)/(f)=(1)/(v_(2))+(1)/(u_(2)),-(1)/(-15)=(1)/(v_(2))-(1)/(20)implies(1)/(v_(2))=(1)/(20)-(1)/(15)`
`v_(2)=-60cm`
So, the image will be shift from mirroe by `(60-24) cm=36cm`.