Question

Two identical glass rods $S_1$ and $S_2$ (refractive index = 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axes (shown by the dashed line) aligned. When a point source of light P is placed inside rod $S_1$ on its axis at a distance of 50 cm from the curved face, the light rays emanating from it are found to be parallel to the axis inside $S_2$. The distance d is

• A. 60 cm
• B. 70 cm
• C. 80 cm
• D. 90 cm

Answer 1

The Correct Option is B

This question is of multiple event. First event on curved surface of $S_1$ & Second on curved surface of $S_2$ Event $- 1\quad n_{2} = 1$ $n_{1}= 1.5$ $\frac{1}{v} - \frac{1.5}{u} = \frac{1-1.5}{R}$ $\frac{1}{v}- \frac{1.5}{-50} = \frac{-0.5}{-10}$ $\frac{1}{v} + \frac{1.5}{50} = \frac{1}{20}$ $\frac{1}{v} = \frac{1}{20}-\frac{1.5}{50}$ $\frac{1}{v} = \frac{5-3}{100} = \frac{2}{100}\quad\quad? v = 50 \,cm$ for second event $\quad u = - \left(d - 50\right)$ $v = 8$ $R = + 10\, cm$ $\frac{1.5}{v}-\frac{1}{u} = \frac{1.5-1}{R}$ $\frac{1.5}{\infty} - \frac{1}{-\left(d-50\right)} = \frac{0.5}{10}$ $\frac{1}{d-50} = \frac{1}{20}$ $20 = d - 50$ $d = 70 \,cm$