Question

A converging mirror M1, a point source S and a diverging mirror M2 a re arranged as shown in figure (18-E4). The source is placed at a distance of 30cm from M1. The focal length of each of the mirrors is 20cm. 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 M

Answer 1

Given :

For first reflection in M

u= -30cm

f= - 20cm

1/v+1/u= 1/f

1/v= 1/30 -`/20= -1/60

v= = -60cm

For second reflection in M

u= 60 - (30+x) = 30 - x

v=x

f=20cm

1/(30-x) -1`/x =1/20

x-30+x/x(30-x) = 1/20

40x-600=30x - x²

x²+10x -600=0

x=-10±50/2

=-10+50/2 = 40/2= 20cm

x= -10-50/2 =-60/2= - 30cm

Total distance between two lines is 20+30 =50cm