Question

The focal length of a convex lens of refractive index $1.5$ is $f$ when it is places in air. When it is immersed in a liquid it behaves as a converging lens its focal length becomes $xf(x>1)$. The refractive index of the liquid

• A. $>3/2$
• B. $<\left(3/2\right)$ and $>1$
• C. $<3/2$
• D. all of these

Answer 1

The correct option is B $<\left(3/2\right)$ and $>1$

$\frac{1}{f}=(n-1)(\frac{1}{R_1}+\frac{1}{R_2})$
$\Rightarrow \frac{1}{f}=(\frac{1.5}{1}-1)(\frac{1}{R_1}+\frac{1}{R_2})$ when the lens is placed in air and
$\frac{1}{xf}=(\frac{1.5}{y}-1)(\frac{1}{R_1}+\frac{1}{R_2})$ when the lens is places in the liquid.
where $y=R.l.$ of the liquid
solving we get, $y=\frac{3}{2+1/x}$
Hence $\left(B\right)$ is correct.