The figure shows an equi-convex lens. What should be the condition of the refractive indices so that the lens becomes diverging?

Options

A. `2mu_(3)gtmu_(1)-mu_(2)`
B. `2mu_(2)ltmu_(1)+mu_(3)`
C. `2mu_(2)gt2mu_(1)_mu_(3)`
D. None of the above

Answer

B

Explanation

(b) We have, `mu_(2)/v_(1)-mu_(1)/oo=(mu_(2)-mu_(1))/R`
and `mu_(3)/f-mu_(2)/v_(1)=(mu_(3)-mu_(2))/(-R)`
From Eqs. (i) and (ii) we get
`mu_(3)/f=(mu_(2)-mu_(1)-mu_(3)+mu_(2))/R=(2mu_(2)-(mu_(1)+mu_(3)))/R`
Lens will become diverging, if f is negative
i.e., `2mu_(2)lt(mu_(1)+mu_(3))`