A short linear object of length b lies along the axis of a concave mirror or focal length f at a distance u from the pole of the mirror. The size of the image is approximately equal to

Options

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

Answer

D

Explanation

Mirror formula
`(1)/(v) + (1)/(u) = (1)/(f) `
On differentiating
`rArr " . - (1)/(v^(2)) dv - (1)/(u^(2)) du = 0 rArr dv = - ((v)/(u))^(2) `du
Since, `(v)/(u) = (f)/(u -f)`
`therefore " " dv = - ((f)/(u -f ))^(2) `l.