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) " and " (I)/(2)`
B. f and `(I)/(4)`
C. `(3f)/(4)" and " (I)/(2)`
D. f and `(3I)/(4)`

Answer

D

Explanation

Intensity (I) `prop ("area")^(2) `
`rArr (I_(1))/(I_(2)) = (pi r^(2))/(pi r^(2) - pi ((r )/(2))^(2) ) = (4r^(2))/(3r^(2)) rArr I_(2) = (3)/(4) I`
Focal length remains unchanged.