Question

Consider a sphere of radius R made of glass of refractive index `mu`. A small object moves along the dismeter with a constant velocity u. Find the velocity of the image as seen by an observer outside when the object passes through center.
A. u
B. `muu`
C. `u//mu`
D. zero

Answer 1

Correct Answer - b.
`(1)/(-y)-(mu)/(-x)=(1-mu)/(-R)rArr (1)/(y)=(1-mu)/(R)+(mu)/(x)`
When object is at center`:x=R`.
Putting`x=R,` we get `y=R`
Differentiating (i), we get
`-(1)/(y^(2))(dy)/(dt)=-(mu)/(x^(2))(dx)/(dt)rArr (dy)/(dt)=mu((y)/(x))^(2)(dx)/(dt)`
`rArrv=mu((R)/(r))^(2)urArrv=muu`