Question

Two symmetric double convex lenses $A$ and $B$ have the same focal length but the radii of curvature differ so that $R_{A}=0.9 R_{B} .$ If $\mu_{A}=1.63,$ then $\mu_{B}$ is

• A. 1.1
• B. 1.5
• C. 1.6
• D. 1.7

Answer 1

Answer: (D)

$\frac{1}{f_{A}}=\left(\mu_{A}-1\right)\left[\frac{1}{R_{A}}-\frac{1}{-R_{A}}\right]=\frac{\left(\mu_{A}-1\right) 2}{R_{A}}$
Similarly, $\frac{1}{f_{B}}=\frac{\left(\mu_{B}-1\right) 2}{R_{B}}$
Given that $f_{A}=f_{B} \Rightarrow \frac{\left(\mu_{A}-1\right) 2}{R_{A}}=\frac{\left(\mu_{B}-1\right) 2}{R_{B}}$
$\Rightarrow \left(\mu_{B}-1\right)=\frac{\left(\mu_{A}-1\right) \cdot R_{B}}{R_{A}}=\frac{(1.63-1) R_{B}}{\left(0.9 R_{B}\right)}=0.7$
or $\mu_{B}=1.7.$