Two identical glass rods and (refractive index = 1.5) have one convex end of radius of curvature 10 cm. They are placed with the curved surfaces at a distance as shown in the figure, with their axes (shown by the dashed line) aligned. [2015]

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 [2015]

Smart Achievers · Accepted Answer

(2)

For refraction in $S_{1}$ ,

$d$ $\Rightarrow - \frac{1.5}{- 50} + \frac{1}{V} = \frac{1 - 1.5}{- 10}$

$\Rightarrow V = 50 cm$

Again, for refraction in $S_{2}$ ,

$- \frac{n_{1}}{u} + \frac{n_{2}}{v} = \frac{n_{2} - n_{1}}{R}$

$- \frac{1}{- (d - 50)} + \frac{1.5}{\propto} = \frac{1.5 - 1}{10}$

$∴$ $\frac{1}{d - 50} = \frac{1}{20}$ $\Rightarrow d - 50 = 20$

$∴$ $d = 70 cm$

Solution

1 60 cm

2 70 cm

3 80 cm

4 90 cm

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