Question

A liquid of refractive index 1.33 is placed between plano-convex lenses with refractive index 1.50. Two possible arrangement of P and Q are shown, the system is

• A. Divergent in P, convergent in Q
• B. Convergent in P, divergent in Q
• C. Convergent in Both
• D. Divergent in Both

Answer 1

The correct option is C Convergent in Both

First case
$P=P_1+P_2+P_3=\left[\right(1.5-1).\{\frac{1}{R}\}\times 2]-\left[\right(1.33-1\left)\right\{\frac{2}{R}\left\}\right]=\frac{2}{R}(0.5-0.33)=+ve$
Second case
$P=P_1+P_2+P_3=\left[\right(1.5-1).\{\frac{1}{R}-0\left\}2\right]-\left[\right(1.33-1\left)\right\{\frac{1}{R}-0\left\}\right]=\frac{1}{R}(1-0.33)=+ve$