A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that the end closer to the pole is 20 cm away from it. Find the length of the image.

Options

A. `10 cm`
B. `15 cm`
C. `2.5 cm`
D. `5 cm`

Answer

D

Explanation

Here, `f = -10 cm`
For end A, `u_(A) = -20 cm`
Image position `v_(A)` of end A is given by
`(1)/(v_(A)) + (1)/((-20)) = (1)/((-10))` or `(1)/(v_(A)) = (1)/(-10) + (1)/(20) = - (1)/( 20 )`
`v_(A) = -20 cm`
For end `B, u_(B) = -30 cm`
Image position `v_(B)` of end b is given by
`(1)/(v_(B)) + (1)/((-30)) = (1)/((-10))` or `(1)/(v_(B)) = (1)/(-10) + (1)/(30) = -(2)/(30)`
`v_(B) = - 15 cm`
Length of image ` = |v_(A)| - |v_(B)|= 20 cm - 15 cm = 5 cm`