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


1