All objects referred to the subsequent problems lie on the principal axis.

In above question if the object is real, then the final image formed after two refractions :

Options

A. may be real
B. may be virtual
C. must be virtual
D. both `A` and `B`

Answer

D

Explanation

Consider object on left side of spherical surface seperating two media.
If real object is in rarer media i.e. `n_(1) lt n_(2)`
Then `(n_(2))/(v)=(n_(2)-n_(1))/((-u))+(n_(1))/(-R)=-ve`
Hence image shall be virtual for a real object lying
on concave side with rarer media....(1)
If real object is in denser media i.e. `n_(1) gt n_(2)`
`(n_(2))/(v)=(-(n_(1)-n_(2)))/((-u))+(n_(1))/((-R))=(n_(1)-n_(2))/(u)-(n_(1))/(R)`
`:.` Image is real if
`(n_(1)-n_(2))/(u) gt (n_(1))/(R)` or `u lt ((n_(1)-n_(2))R)/(n_(1))`.....(2)
and image is virtual if `u gt((n_(1)-n_(2))/(n_(1)))R`...(3)
From statements `1,2` and `3` we can easily conclude the answers.