A thin lens focal length `f_(1)` and its aperture has diameter `d`. It forms an image of intensity `I`. Now the central part of the aperture up to diameter`(d)/(2)` is blocked by an opaque paper. The focal length and image intensity will change to

Options

A. `f//2,I//2`
B. `f,I//4`
C. `3f//4,I//2`
D. `f,3I//4`

Answer

D

Explanation

`Iprop aperture^(2)`
`I_(1) prop pid^(2)//4 rArr I_(2)prop(pid^(2)//4-pi(d//4)^(2))`
`I_(2)prop(pid^(2))/(4)(1-(1)/(4)) rArr I_(2)prop (3)/(4).(pid^(2))/(4)`
`(I_(2))/(I_(1))=(3)/(4) rArrI_(2)=(3)/(4)I_(1)`