Question

The equiconvex lens shown in figure is silvered on one side. For what distance of object from the lens is the image formed on the object itself?

(1) \(\mu R\)

(2) \(\frac{R}{\mu}\)

(3) \(\frac{R}{2\mu - 1}\)

(4) \(\frac{R}{2 \mu - 2}\)

Answer 1

Correct option is : (3) \(\frac{R}{2\mu - 1}\)

Silvering of lens

\(\frac{1}{F_{eq}} = \frac{1}{f_m} - \frac{2}{f_{\ell}}\quad \frac{1}{f_{\ell}} = (\mu - 1)\left(\frac{1}{R} - \left(\frac{1}{-R}\right)\right)\) 

 \( = \frac{-2}{R} - \frac{4(\mu - 1)}{R}\quad \frac{1}{f _{}\ell} = \frac{2(\mu - 1)}{R}\)