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

Answer

B

Explanation

For `S_(1)` (Refraction from denser to rarer medium)
`u = - 50 cm, R = - 10 cm`
`(mu_(2))/(-u) + (mu_(1))/(v) = (mu_(1) - mu_(2))/(R )`
`(3//2)/(-(-50)) + (1)/(v) = (1 - 3//2)/(-10) or (1)/(v) + (3)/(100) = (1)/(20)`
`(1)/(v) = (1)/(20) - (3)/(100) = (1)/(50)`
`v = 50 cm`
for `S_(2)` Refraction from rarer to denser medium
`:. u rarr - (d - 50), v = oo, R_(2) = R`
`(mu_(1))/(- u) + (mu_(2))/(v) = (mu_(2) - mu_(1))/(R )`
`(1)/((d - 50)) + (3//2)/(oo) = (1)/(20)`
`d = 70 cm`