Question

A biconvex lens has focal length f and intensity of light I passing through it. What will be the focal length and intensity for portions of lenses obtained by cutting it vertically and horizontally as shown in the figure?

Answer 1

R₁ = R

R₂ = - R

Vertically-

`1/"f" = (mu - 1)(1/("R"_1)_(-> "R") - 1/("R"_2)_(->-"R"))`

`1/"f" = (mu - 1) 2/"R"`   ...(1)

`1/"f"_"p" = (mu - 1)(1/(∞_(-> 0)) - (- 1/"R"))`

`1/"f"_"p" = (mu - 1)/"R"`   ....(2)

equation (1) ÷ equation (2)

`(1/"f")/(1/"f"_"p")` = 2

`"f"_"p"/"f"` = 2

`"f"_"p"` = 2f

Horizontally-

`1/"f'" = (mu - 1)(1/("R"_1)_(-> "R") - 1/("R"_2)_(->-"R"))`

`1/"f'" = (mu - 1) 2/"R"`   ...(3)

f' = f