Question

A diverging lens of focal length F is cut into two identical parts , each forming a plano concave lens. What is the focal length of each part?

Answer 1

lens is diverging , it means concave lens

F = - R/2( u -1) --------(1)

where R is radius of curvature of lens , u is refractive index of lens with respect to medium .

if we cut ,then each part wil be plano-concave lens.
1/f = ( u -1){ 1/R1 - R2}

For plano-concave lens
R1 = ∞
R2 = R

1/f = ( u -1){ 1/∞ - 1/R}

1/f = -( u -1)/R

f = -R/( u -1)

from equation (1)

f = 2F

hence , focal length of plano -concave lens will be double of concave lens
e .g f = 2F