Q58 / 58 · KVPY 2016 (SA) · Physics
A hollow lens is made of thin glass and in the shape of a double concave lens. It can be filled with air, water of refractive index $1.33$ or $\mathrm{CS}_{2}$ of refractive index $1.6$. It will act as a diverging lens if it is
- Afilled with air and immersed in water.
- Bfilled with water and immersed in $\mathrm{CS}_{2}$.
- Cfilled with air and immersed in $\mathrm{CS}_{2}$
- Correct answerDfilled with $\mathrm{CS}_{2}$ and immersed in water.
Solution
$\mu_{\text {air }}=1$
$\mu_{\text {water }}=1.33$
$\mu_{\mathrm{cs}_{2}}=1.6$
$\begin{array}{l} \frac{1}{\mathrm{f}}=\left(\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}}-1\right)\left[-\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right] \\ \frac{1}{\mathrm{f}}=-\left(\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}}-1\right)\left[\frac{1}{\mathrm{R}_{1}}+\frac{1}{\mathrm{R}_{2}}\right] \end{array}$ for diverging lens $\mathrm{f}$ must be $-\mathrm{ve}$. $\therefore$ for this $\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}}>1$ $\mathrm{n}_{2}>\mathrm{n}_{1}$ $\therefore$ Lens should be filled with liquid which has more refractive index in comparison to liquid in which lens is immersed. $\therefore$ Ans (D) is the correct option as $\mu_{\alpha_{2}}>\mu_{\text {water }}$
$\begin{array}{l} \frac{1}{\mathrm{f}}=\left(\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}}-1\right)\left[-\frac{1}{\mathrm{R}_{1}}-\frac{1}{\mathrm{R}_{2}}\right] \\ \frac{1}{\mathrm{f}}=-\left(\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}}-1\right)\left[\frac{1}{\mathrm{R}_{1}}+\frac{1}{\mathrm{R}_{2}}\right] \end{array}$ for diverging lens $\mathrm{f}$ must be $-\mathrm{ve}$. $\therefore$ for this $\frac{\mathrm{n}_{2}}{\mathrm{n}_{1}}>1$ $\mathrm{n}_{2}>\mathrm{n}_{1}$ $\therefore$ Lens should be filled with liquid which has more refractive index in comparison to liquid in which lens is immersed. $\therefore$ Ans (D) is the correct option as $\mu_{\alpha_{2}}>\mu_{\text {water }}$
Hence, the correct answer is option: 'D'.