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

Answer

C

Explanation

Image position of end A
`(1)/(v_(A))+(1)/(-20)=(1)/(-10)`
`v_(A)=-20cm`
Image position of the end B
`(1)/(v_(B))+(1)/(-30)=(1)/(-10)`
`(1)/(v_(B))=-(1)/(15)`
`v_(B)=-15cm`
Length of the image is
`L_(A'B')=|v_(A)|-|v_(B)|=20-15=5cm`