A diverging lens of focal length `F` is cut into two idential parts, each forming a plano concave lens, 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 shown in Fig.,
`R_1 = -R` and `R_2 = oo`
`:. (1)/(F_1)=(1)/(F_2)=(mu - 1)((1)/(-R) - (1)/(oo)) = (-(mu - 1))/( R)`
=`(1)/(2 F)`
`:. F_1 = F_2 = 2 F`.
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