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

End `A` of the rod acts as an object for mirrorr and `A^(')` will be its image. By mirrorr formula, image distance of `A`.
Now using `(1)/(f)=(1)/(v)+(1)/(u)`
`u=2f+10=-30cm`
`implies(1)/(-10)=(1)/(v_(A))+(1)/((-30))`
`impliesv_(A)=-15cm`
Also image distance of `C`
`v_(C)=-20cm`
The length of image `=|v_(A)-v_(C)|`
`=|-15-(-20)|=5cm`
`:.` Length of image is `5cm`.