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 f_{o} the diverging lens is, f_{0} = - 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

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