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. Whee should an object be placed before this lens so that the image is formed on the object itself?

Answer

`12.5 cm`

Explanation

In Fig., let the object be placed at `O` The ray `OA` is refracted along `AB` at first surface and hits the silvered surface. To get the final image at `O, AB` should fall normally on silvered surface. Therefore, `AB` should appear to come from centre of curvature `C_2` of second surface.
Thus `v = -25 cm`,
`R = + 25 cm, mu_1 = 1, mu_2 = 1.5`.
Refraction from rarer to denser medium
`-(mu_1)/(mu)+(mu_2)/(v)=(mu_2 - mu_1)/( R)`
Solve to get `u = -12.5 cm`
Thus the object should be placed at a distance of `12.5 cm` to the left of the lens.
.