An equiconvex lens of refractive index `n_(2)` is placed such that the refractive index of the surrouding media is as shown. The lens :

Options

A. must be diverging if `n_(2)` is less than the aritmetic mean of `n_(1)` and `n_(3)`
B. must be converging if `n_(2)` is greater than the arithmetic mean of `n_(1)` and `n_(3)`
C. may be diverging if `n_(2)` is less than the arihmetic mean of `n_(1)` and `n_(3)`
D. will neither be diverging nor converging if `n_(2)` is equal to arithmetic mean of `n_(1)` and `n_(3)`

Answer

a,b,d

Explanation

`f=(n_(1)R)/(2n_(2)-n_(1)-n_(3))` or `(n_(3)R)/(2n_(2)-n_(1)-n_(3))`
if `n_(2)lt(n_(1)+n_(3))/(2)rArrf is -ve rArr` lens is diverging
if `n_(2)gt(n_(1)+n_(3))/(2) rArrf is+ve rArr` lens is converging.
If `n_(2)=n_(1)+n_(2) rArr f=infty` neither converging nor diverging.