An object is placed 30cm away from a convex lens of focal length 10cm and a sharp image is formed on a screen. Now, a convex lens is placed In contact with the convex lens. The screen now has to be moved by 45cm to get a sharp image again. The magnitude of focal length of the convex lends in (in cm)

Options

A. 72
B. 60
C. 36
D. 20

Answer

D

Explanation

For the best first condition, `f_(1)=10cm u=-30cm`
then, `(1)/(f_(1))=(1)/(v)-(1)(u) Rightarrow=(1)/(v)+(1)/(30)`
`(1)/(v)=(1)/(10)-(1)/(30) Rightarrow v=(30)/(2)=15`
For the second condition, when concave lens is placed,
(where F=focal length of combination)
`therefore(1)/(F)=(1)/(60)+(1)/(30)=F=(60)/(3)=20cm`
The magnitude of focal length of concave lens,
`(1)/(F)=(1)/(f_(1))+(1)/(f_(2)) Rightarrow (1)/(20)=(1)/(10)+(1)/(f_(2))`
`f_(2)`=-20(negative sign for concave lens)