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 emenating from it are found to be parallel to the axis inside `S_(2)`. The distance d is

Options

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

Answer

B

Explanation

For refraction in `S_(1)`
`-(n_(1))/(u)+(n_(2))/(v)=(n_(2)-n_(1))/(R)implies-(1.5)/(-50)+(1)/(V)=(1-1.5)/(-10)impliesv=50` cm.
For refraction is `S_(2)`
`-(n_(1))/(u)+(n_(2))/(v)=(n_(2)-n_(1))/(R)`
`(1)/(-(d-50))+(1.5)/(propto)=(1.5-1)/(10)`
`:'``(1)/(d-50)=(1)/(20)`
`:'``d=70cm`
B is the correct option.