An object to the left of a lens is imaged by the lens on a screen `30cm` to the right of the lens. When the lens is moved ` 5cm` to the right, the screen must be moved `5cm` to the left to refocus the images. The focal length of lens is :-

Options

A. `10cm`
B. `15cm`
C. `20cm`
D. `30cm`

Answer

A

Explanation

`(1)/(30)=(1)/(f)-(1)/(u)`
`u^(')=u+5`
`v^(')=20`
`(1)/(20)+(1)/(u+5)=(1)/(f)`
`(1)/(30)+(1)/(u)=(1)/(20)+(1)/(u+5)`
`impliesu^(2)+5u-300=0`
`u=15cm(or)-20cm`
`therefore u =15cm`
`(1)/(f)=(1)/(30)+(1)/(15)=10cm`