A converging mirror M1, a point source S and a diverging mirror M2 are arranged as shown in figure (18-E4). The source is placed at a distance of 30 cm for M1. The focal length of each of the mirrors 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 two mirrors. (b) Find the location of the image formed by the single reflection from M2.

(a) 50 cm (b) 10 cm from the diverging mirror farther from the converging mirror

The mirror M1 is converging mirror and M2 is diverging

mirror. The focal length of both the mirrors is same, i.e. 20cm, and the image is also formed at the focus after the reflection from both the mirror surfaces.

For mirror M1,

The distance of object from the mirror, u= -30cm (converging mirror)

Focal length, f= -20cm

Using mirror formula,

For mirror M2

the object distance from the mirror will be the difference of the image formed by first mirror and the distance between the two mirrors, i.e. u= 60 - (30 + x) cm = 30-x cm

the distance of image from the mirror, v= -x cm

focal length of the mirror, f= 20cm

using mirror formula

Hence, total distance between the two lines is 20+30 = 50 cm