A transparent sphere of radius `R` and refractie index `mu` is kept in air. At what distance from the surface of the sphere shold a point object be placed so as to form a rea image at the same distance from the sphere?

Options

A. `muR`
B. `(R)/(mu-1)`
C. `(R)/(mu+1)`
D. `(R)/(mu)`

Answer

B

Explanation

As `P_(1)O=P_(2)I`, therefore, the rays must pass through the sphere in a direction parallel to the optic axis, as shown in the figure.

Now, for first refraction at A from rarer to denser meduim,
`-(mu_(1))/(u)+(mu_(2))/(v)=(mu_(2)-mu_(1))/(R)implies(1)/(u)+(mu)/(oo)=(mu-1)/(R)`
`:. u=-(R)/((mu-1))` or `|u|=(R)/((mu-1))`