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

First let us find the location of image when light ray emerges from first cylinder using refraction formula. Note that this refraction is from glass to air
`mu_2/v-mu_1/u=(mu_2-mu_1)/R`
`implies 1/v-(1.5)/(-50)=(1-1.5)/(-10)`
`implies1/v+3/100=5/100`
`implies 1/v =2/100`
`implies v = 50 cm`

Distance between cylinders, d must be greater than 50 cm so that convex surface further may converge it to make it parallel to axis when it enters into formula for the desired refraction .
`mu_2/v-(mu_1)/u=(mu_2-mu_1)/R`
`implies(1.5)/(oo)-(1)/(-(-d-50))-(1.5-1)/(+10)`
`implies (1)/((d-50))=1/20`
`rArr" "d-50=20`
`rArr" "d=70cm.`
Hence, option (b) is correct.