Question

Two convex lenses, each of focal length 10 cm, are placed at a separation of 15 cm with their principal axes coinciding. (a) Show that a light beam coming parallel to the principal axis diverges as it comes out of the lens system. (b) Find the location of the virtual image formed by the lens system of an object placed far away. (c) Find the focal length of the equivalent lens. (Note that the sign of the focal length is positive although the lens system actually diverges a parallel beam incident on it.)

Answer 1

Two convex lenses, each of focal length 10 cm, are placed at a separation of 15 cm with their principal axes coinciding. (a) Show that a light beam coming parallel to the principal axis diverges as it comes out of the lens system. (b) Find the location of the virtual image formed by the lens system of an object placed far away. (c) Find the focal length of the equivalent lens. (Note that the sign of the focal length is positive although the lens system actually diverges a parallel beam incident on it its too lendy

Answer 2

Given :

f1=10cm

f2=10cm

distance between two lenses=15cm

a) As shown in attachment :

the light rays are incident parallel to principal axis on fist lens.

The rays will converge within focus of second lens .

hence all the rays emerging from lens are diverging

b)1/f=1/v-1/u

1/v= 1/f+1/u

1/v=1/10+1/in

1/v=1/10

v= 10cm

For second lens :

u= -(15-10)= -5cm

1/v=1/f+1/u

1/v=1/10-1/5=1-2/10=-1/10

Thus virtual image of object will be at 5cm from the first convex lens .

c) equivalent focal length :

1/F=1/f1+1/f2-d/f1f2

here f=f1=f2=10cm

1/F=1/10+1/10- 15/100

1/F=20-15/100=5/100

F=20cm