Let `f_(v)` and `f_(r)` are the focal lengths of a convex lens for violet and red lights respectively. If `F_(v)` and `F_(r)` are the focal lengths of a concave lens for violet and red light respectively, then

Options

A. `f_(v) lt f_(r)` and `F_(v) gt F_(r)`
B. `f_(v) lt f_(r)` and `F_(v) lt F_(r)`
C. `f_(c) gt f_(r)` and `F_(v) gt F_(r)`
D. `f_(v) gt f_(r)` and `F_(v) lt F_(r)`

Answer

B

Explanation

According to lens makers formula
`(1)/(f)=(mu-1)((1)/(R_(1))+(1)/(R_(2)))implies(1)/(f)prop (mu-1)`
Since `mu_(Red) lt mu_("violet") rArr f_(v) lt f_(r)` and `F_(v) lt F_(r)`
Always keep in mind that whenever you asked to compare ( greater than or less than ) `u,v ` or f you must not apply sign conventions for comparison.