Question

A converging lens and a diverging mirror are placed at a separation of 15 cm. The focal length of the lens is 25 cm and that of the mirror is 40 cm. Where should a point source be placed between the lens and the mirror so that the light, after getting reflected by the mirror and then getting transmitted by the lens, comes out parallel to the principal axis?

Answer 1

Given :

distance between convex lens and mirror =15cm

focal length of lens = 25cm

focal length of mirror = 40cm

Let x cm be the object distance from mirror.

u=-x

V=25-25=10cm

f=40cm

from lens formula :

1/f=1/v-1/u

1/x= 1/10 -1/40 =4-1/40

x= 40/3

Thus object distance = 15- 40/3= 5/3 cm= 1.67cm from lens

Answer 2

distance between convex lens and mirror =15cm

focal length of lens = 25cm

focal length of mirror = 40cm

Let x cm be the object distance from mirror.

u=-x

V=25-25=10cm

f=40cm

from lens formula :

1/f=1/v-1/u

1/x= 1/10 -1/40 =4-1/40

x= 40/3

Thus object distance = 15- 40/3= 5/3 cm=1.67cm from lens

Hope it helps------