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

Options

A. `2 mu_3gtmu_1-mu_2`
B. `2 mu_2ltmu_1+mu_3`
C. `2 mu_2gt 2mu_1-mu_3`
D. None of these

Answer

B

Explanation

Refraction from first surface,
`mu_2/v_1-mu_1/oo=(mu_2-mu_2)/(+R)`
Refraction from second surface,
`mu_3/f-mu_2/v_1=(mu_3-mu_2)/(-R)` , (as `v_2=f`)
Adding these two equations, we get
`mu_3/f=(mu_2-mu_1)/R-(mu_3-mu_2)/R`
Lens becomes diverging if f is negative or
`mu_3-mu_2gtmu_2-mu_1`
or `mu_3+mu_2gt2mu_2`
Same result is obtained if parallel beam of light is
incident from RHS.