## Question

A thin equiconvex lens has focal length 10 cm and refractive index 1.5. One of its faces is now silvered and for an object placed at a distance *u* in front of the lens, the image coincides with the object. The value of *u* is:

### Solution

5 cm

The radius of curvature of silvered face is given by

The rays refracted at the un-silvered face will be incident along the radius of the silvered face. So, the virtual image formed by the lens is at the centre of curvature of the silvered face. As *R* = 10 cm so, *v* = +10 cm. Now

Solving, we get

#### SIMILAR QUESTIONS

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The plane face of a plano-convex lens of focal length 20 cm is silvered. What type of mirror will it become and of what focal length *f *?