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

Options

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

Answer

D

Explanation

As `(1)/(u) + (1)/(v) = (1)/(f)`, differentiating we get
`-(1)/(u^(2))(s u)/(d t) - (1)/(v^(2))(d v)/(d t) = 0` or `(d v)/(d u) = -(v^(2))/(u^(2))`
or `m = (h_(2))/(b) = (v^(2))/(u^(2))` or `h_(2) = b((v^(2))/(u^(2)))`
`h_(2) = b((f)/(u - f))^(2) [as m = (v)/(u) = (f)/(u - f)]`