Two identical glass rods ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ (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 $\mathrm{P}$ is placed inside rod ${\mathrm{S}}_1$ 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 ${\mathrm{S}}_2$ . The distance $\mathrm{d}$ is

• A

  60 cm
• Correct answer
  B

  70 cm
• C

  80 cm
• D

  90 cm

Solution

For first surface
$\frac{1}{\mathrm{v}}-\frac{1.5}{-50}=\frac{1-1.5}{-10}$
$\mathrm{v}=50\mathrm{ }\mathrm{c}\mathrm{m}$
For second surface
$\frac{1.5}{\mathrm{\infty }}-\frac{1}{-\left(\mathrm{d}-50\right)}=\frac{1.5-1}{10}$
$\mathrm{d}=70\mathrm{ }\mathrm{c}\mathrm{m}$

Hence, the correct answer is option: 'B'.