Question

Figure shows a concavo - convex lens $\mu_2$. What is the condition on the reflective indices so that the lens is diverging?

• A. $2 \mu_3 < \mu_1+\mu_2$
• B. $2 \mu_3 > \mu_1+\mu_2$
• C. $\mu_3 > 2\left(\mu_1-\mu_2\right)$
• D. $\text { none of these }$

Answer 1

Answer: (B)

$\frac{\mu_2}{V}-\frac{\mu_1}{-u_0}=\frac{\mu_2-\mu_1}{-2 R}$
$\frac{\mu_3}{ V _{ f }}-\frac{\mu_2}{ V }=\frac{\mu_3-\mu_2}{- R }$
$\frac{\mu_3}{ V _{ f }}+\frac{\mu_1}{u_0}=\frac{\mu_1-\mu_2}{2 R }+\frac{\mu_2-\mu_3}{R}$
$\therefore \frac{\mu_1-\mu_2}{2}<\mu_3-\mu_2 $
$\Rightarrow \mu_1-\mu_2< 2 \mu_3-2 \mu_2$
$\Rightarrow \mu_1+\mu_2<2 \mu_3$