A short linear object of length b lies along the axis of a concave mirror of focal length fat a distance u from the pole of the mirror, what is the size of image?

Options

A. `b((u-f)/(f))^(1//2)`
B. `b((f)/(u-f))`
C. `b((u-f)/(f))`
D. `b((f)/(u-f))^(2)`

Answer

D

Explanation

u = -u, f=-f `v_(B) = (uf)/(f-u)`
`v_(C) = ((u-b)f)/(f-(u-b))`
`v_(B) - v_(C) = (uf)/(f-u) - ((u-b)f)/(f-u +b)`
=`(ub)/(f-u)- (uf)/(f-u+b) + (bf)/(f-u +b) = b((f)/(u-f))^(2)`