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A converging lens of focal length 12 cm and a diverging mirror of focal length 7.5 cm are placed 5 cm apart with their principal axis coinciding. Where should an object be placed so that the image would fall on itself?
Given:
The focal length of the lens, f= 12cm
And the focal length of diverging mirror= -7.5cm
Let us assume that the object be placed at a distance x from the lens
For convex lens:
u= -x
f= -12cm
Now applying the lens formula:
This image act as the object for the concave mirror. For the mirror,
For mirror:
The focal length fo the diverging lens is, f0 = - 7. 5cm
From mirror formula:
For second refraction in concave lens:
v=+x
Using the lens formula,
On rearranging the above equation, we get,
25x �- 1400x-6000=0
x �-56x-240=0
(x-60)(x+4)=0
x= 60cm
The object should be placed at a distance of 60cm from lens farther away from mirror so that final image is formed on itself