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`.
.