Question

A thin rod of length f/3 is placed along the optical axis of a concave mirror of focal length f such that its image which is real and elongated just touches the rod. calculate the magnification. (answer is 3/2)

Answer 1

Since the image touches the rod, one end of the rod must be at C of the mirror.

Since the image is real and elongated, the other end of the rod must be between C and F of the mirror.

The distance of this latter ( A) end from the optic center of the mirror is (R-f/3) = 2f-f/3

= 5f/ 3

(u –f)= 5f/ 3-f = 2f/3

m = f/ (u-f) = 3/2 = 1.5

Magnification of the A end of the rod is 1.5 where as the magnification of the joint of image and rod is 1.