Question

Determine the focal length of a concave mirror if: 

(a) with the distance between an object and its image being equal to l = 15 cm, the transverse magnification β = —2.0; 

(b) in a certain position of the object the transverse magnification is β₁ = —0.50 and in another position displaced with respect to the former by a distance l = 5.0 cm the transverse magnification β₂ = —0.25.

Answer 1

(a) From the mirror formula, 

        ........ (1)

In accordance with the problem

From these two relations, we get :

Substituting it in the Eqn. (1),

Now , it is clear from the above equation, that for smaller β , s must be large, so the object is displaced away from the mirror in second position.

Eliminating s from the Eqn. (2) and (3), we get,