Question

The effective focal length of the lens combination shown in figure is $-60\text{cm}$. The radii of curvature of the curved surfaces of the plano-convex lenses are $12\text{cm}$ each and refractive index of the material of the lens is $1.5$. The refractive index of the liquid is:

• A. $1.42$
• B. $1.33$
• C. $1.53$
• D. $1.60$

Answer 1

The correct option is D $1.60$

Given, $F=-60\text{cm};R=12\text{cm}$ ${\mu }_s=1.5$

Given lens ia combination of three lens.
$\frac{1}{F}=\frac{2}{f_s}+\frac{1}{f_l}$

$\Rightarrow \frac{1}{-60}=2({\mu }_s-1)\frac{1}{R}+({\mu }_l-1)(-\frac{2}{R})$

$\Rightarrow \frac{1}{-60}=\frac{2{\mu }_s}{R}-\frac{2}{R}-\frac{2{\mu }_l}{R}+\frac{2}{R}$

$\Rightarrow \frac{1}{-60}=\frac{2}{R}({\mu }_s-{\mu }_l)=\frac{2}{12}[1.5-{\mu }_l]$

$\Rightarrow \frac{1}{-10}=1.5-{\mu }_l$

$\Rightarrow {\mu }_l=1.5+0.1=1.60$

$\Rightarrow {\mu }_l=1.60$