Question

Moon light passes through a converging lens of focal length
19 cm, which is 20.5 cm from a second converging lens of fo-
cal length 2 cm. Where is the image of the moon produced by
the lens combination?​

Answer 1

Explanation:

Let,

the lens be placed at x distance from first source.

for 1st source:

Object distance u=x cm

focal length, f=9cm

f

1

=

v

1

−

u

1

(from lens formula)

⇒

9

1

=

v

1

+

x

1

⇒v=

x−9

9x

....(1)

for second source:

Object distance, u=24−x

focal length, f=9cm

⇒

9

1

=

−v

1

+

24−x

1

(from lens formula)

⇒v=9(2y−x)/x−15....(2)

Equating (1) and (2) as LHS is equal,

x−9

9x

=

x−15

9(2y−x)

On solving

x=6cm or x=18cm

Hope this helps mate ☺️.