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 cuved face, the light rays emanating from it are found to be paralle to the axis inside `S_(2)` . The distance `d` is :

Options

A. 60 cm to the left of the system
B. 70 cm
C. 80 cm
D. 90 cm

Answer

B

Explanation

For first surface
`(1)/(V) - (1.5)/(-50) = (1 - 1.5)/(-10) implies V = 50 cm `
for second surfaces
`(1)/(oo) - (1)/(-(d - 50)) = (1.5 -1)/(10)`
d = 70 cm `" " therefore (B)`