Question

2
Two identical objects are in a straight line and distance between them is 24 cm.
Where should a converging lens of focal length of 9cm be placed between the two
objects, so that images of both the objects are formed at the same point on the
principal axis?​

Answer 1

Explanation:

Distance between the two sources = d = 24 cm

f = 9 cm

Consider that the lens is separated from the first object at a distance 'x' cm.

From the first ource and using the lens formula

1/f = 1/u+1/v

1 /9 = 1/ х +1/v

....... (Equation 1)

Similarly for second point of source, we have

= 1/9=1/ 24-X+1/v

+ V . (Equation 2).....(x + y, = 24)

Adding equation 1 and 2 and solving the quadratic equation, we (x -6) (x - 18) = 0

+x = 6 or x = 18

Thus, the lens should be placed at 6 cm or 18 cm.