Question

A Plano-convex lens has a thickness of $4$cm When placed on a horizontal table, with the curved surface in contact with it, the apparent depth of the bottommost part of the lens is found to be $3$cm. If the lens is inverted so that plane face is in contact with the table the apparent depth is found to be $\frac{25}{8}$ cm. The focal length of the lens is

• A. $75cm$
• B. $50cm$
• C. $60cm$
• D. $45cm$

Answer 1

The correct option is A $75cm$

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{\mu }=\frac{{\mu }_2-{\mu }_1}{R}$ $\mu =\frac{4}{3}$

$\frac{8}{25}-\frac{4}{3\times 4}=\frac{-1}{3R}$

$\Rightarrow R=25cm$

$\frac{1}{f}=[\frac{4}{3}-1]\left[\frac{1}{R_1}\right]$

$\frac{1}{f}=\frac{1}{3R_1}$

$f=3R=3\times 25=75cm$