A thin rod of length `(f/3)` is lying along the principal axis of a concave
mirror of focal length f.Image is real , magnified and inverted and one of the end or rod coincides with its image itself. Find length of the image.

Options

A. `(f)/(2)`
B. `(f)/(4)`
C. `2f`
D. `f`

Answer

A

Explanation

One to end of image and object is same i.e., either A or B is centre of curvature. Sunce image is elongated i.e., rod is placed right of centre of curvature hence B is centre of cuvature. Image of B is formed on B it self.
Image of `A`:
`u=((2f-f)/(3))=(-5f)/(3),f=-f,v=?`
`(1)/(v)+(1)/((-5f)/(3))=(1)/(-f)implies(1)/(v)=-(1)/(f)+(3)/(5f)=(-5+3)/(5f)`
`v=-(5f)/(2)`
image length `A^(')B^(')=((5f)/(2-2f))=(f)/(2)`