A point object `O` is kept at a distance `OP=u` The radius of curvature of the spherical surface APB is `CP=R` The refractive index of the media are `n_1` and `n_2` which are as shown in the diagram . Then,
(A) if `n_1gtn_2`, image is virtual for all values of u
(B) if `n_2=2n_1` image is virtual when `Rgtu`
(C) The image is real for all values of `u`, `n_1` and `n_2` here, the correct statements is/are

Options

A. only (B)
B. both (A) and (B)
C. only (A)
D. (A),(B) and (C)

Answer

B

Explanation

`(n_2)/(v)-(n_1)/(u)=(n_2-n_1)/(R)`
`u=-u,R=R`
`(n_2)/(v)-(n_1)/(-u)=(n_2-n_1)/(R)`
`(n_2)/(v)=(n_2-n_1)/(R)-(n_1)/(u)`
if `n_1gtn_2,(n_2)/(v)=-veimpliesv=-ve` (A) is O.K.
if `n_1=2n_1,(n_2)/(v)=(n_1)/(R)-(n_1)/(u)=-ve`, if `Rgtu`.
(B) is O.K.