Question

A converging mirror M₁, a point source S and a diverging mirror M₂ are arranged as shown in the figure. The source is placed at a distance of 30 cm from M₁. The focal length of each of the mirror is 20 cm. Consider only the images formed by a maximum of two reflections. It is found that one image is formed on the source itself. 

(a) Find the distance between the mirrors 

(b) Find the location of the image formed by the single reflection from M₂.

Answer 1

For mirror M₁: u = -30 cm, f = -20 cm By mirror formula, (1/u) + (1/v) = (1/f), we have

(1/-30) + (1/v) = (1/-30) 

which on solving gives, v = -60 cm 

For mirror M₂: The image formed by mirror M₁ is a virtual object for mirror M₂. Let it is a distance x from the pole of mirror M₂.

 Thus u₂ = +x, v₂ = - (30-x) 

Again by mirror formula. We have 

(1/x) + (1/-(30-x)) = (1/20) 

which on solving gives 

x = 10 cm or 60 cm, x = 60 cm is not possible, thus x = 10 cm. 

(a) Thus the separation between the mirrors = 60-10= 50 cm 

(b) The image formed by mirror M₂ is at a distance 10 cm