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`

In Fig.
`AB` is a rod of length `10 cm` lying along principal axis of concave mirror with pole at `P`.
`u_(1) = PA = - 20 cm` and `u_(2) = PB = - 30 cm`
Using mirror formula,
`(1)/(v_(1)) = (1)/(f) - (1)/(u_(1)) = (1)/(-10) + (1)/(20) = (-2 + 1)/(20) = -(1)/(20)`,
`v_(1) = - 20 cm`
`:.` Image of end `A` of rod is at `A` itself.
Similarly, `v_(2) = -15 cm = PB'`
Length of image of the rod `= A' B' = PA' - PB'`
`= 20 - 15 = 5 cm`