Two identical glass rods $S_{1}$ and $S_{2}$ (refractive index =1.5) have one convex end of radius of curvature 10cm. They are placed with the curved surfaces at a distance d as shown in the figure, with their axis (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 50cm 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

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80cm

70cm

90cm

60cm

answer is B.

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Detailed Solution

$\begin{array}{l} \begin{array}{l} R = 10 c m \\ μ = 1.5 \\ R o d 1 : \frac{1}{v} - \frac{1.5}{- 50} = \frac{1 - 1.5}{- 10} \\ \Rightarrow \frac{1}{v} + \frac{1.5}{50} = \frac{0.5}{10} \\ \Rightarrow \frac{1}{v} = \frac{0.5}{10} - \frac{1.5}{50} = \frac{2.5 - 1.5}{50} \\ \Rightarrow v = 50 \end{array} \\ R o d 2 : \frac{1.5}{\infty} - \frac{1}{- (d - 50)} = \frac{1.5 - 1}{10} \\ \Rightarrow \frac{1}{d - 50} = \frac{1}{20} \\ \Rightarrow d = 70 \end{array}$