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

Explanation

For single diverging lens,
`(1)/(F) = (mu -1)((1)/(R_(1)) - (1)/(R_(2)))`
Let `R_(1) = - R, R_(2) = R`
`:. (1)/(F) = (mu -1)((1)/(- R)-(1)/(R )) = (-2(mu - 1))/(R )`
For each half (which is plano concave), as shwon in Fig.,
`R_(1) = - R and R-(2) = oo`
`:. (1)/(F_(1)) = (1)/(F_(2)) = (mu -1)((1)/(R_(2)) - (1)/(oo)) = (-(mu -1))/( R)`
`= (1)/(2 F)`
`:. F_(1) = F_(2) = 2 F`