A curved surface of radius R separates two medium of refractive indices `mu_(1) "and" mu_(2)` as shown in figures A and B .

Identity the correct statement(s) related to the formation of images of a real object O placed at x from the pole of the concave surface, as shown in figure B

Options

A. if `mu_(2) gt mu_(1)`, then virtual image is formed for any value of x
B. if `mu_(2) gt mu_(1)`, then virtual image is formed if `x lt (mu_(1)R)/(mu_(1)-mu_(2))`
C. if `mu_(2) gt mu_(1)`, then real image is formed for any value of x
D. None of these

Answer

B,C

Explanation

v gt0
`therefore (mu_(2))/(v) = (mu_(2)-mu_(1))/(-R) + (mu_(1))/(u) gt "and if" mu_(2) lt mu_(1)`
`(mu_(1)-mu_(2))/(R)- (mu_(1))/(x) gt 0, (mu_(1) - mu_(2))/(R) gt (u_(1))/(x)`
`therefore x gt (mu_(1)R)/(mu_(1)- mu_(2)) therefore (B) "if" mu_(2) lt mu_(1)`,
Then virtual image is formed of `x lt (mu_(1)R)/(mu_(1)-mu_(2))`