A biconvex thin lens is prepared from glass `(mu=1.5)`, the two bounding surfaces having equal radii of 25 cm each. One of the surfaces is silvered from outside to make it reflecting. Where should an object be placed before this lens so that the image is formed on the object itself?

Explanation

Refer to ure. The object is placed at O. A ray OA starting from O gets refracted into the glass at the first surface and hits the silvered surface along AB. To get the image at the object, the rays should retrace their path after reflection from the silvered surface. This wil happen only if AB falls normaly on the silvered `C_2` of the second surface. Thus, due to the refraction at the first surfce a virtual image of O is formed at `C_2` . For this case
`v=PC_2=-25cm, R=PC_1=+25cm, mu_1=1, mu_2=1.5, ` We have `mu_2/v-mu_1/u=(mu_1-mu-2)/R`
`or 1.5/(-25cm)-1/u=(1.5-1)/(25cm)`
`or 1/u=1.5/(25cm)-0.5/(25cm)`
`or, 1/u=-1.5/(25cm)-0.5/(25cm)`
`or,u=-12.5cm`
Thus, the object should be placed at a distance of 12.5 cm from the lens.