Question

An equi-concave lens have power P find power of plano-concave lens when given lens is cut in such a way that two plano-concave lens are formed:
P
P/2
2P
P/4​

Answer 1

Explanation:

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Answer 2

An equi - convex lens have power P. now equi - convex lens is cut in such a way that two plano - concave lens are formed.

To find : The power of plano convex lens.

solution : focal length of equi- convex lens , f = 1/power of lens = 1/P

using lens maker formula,

1/f = (μ - 1)[1/R₁ - 1/R₂]

for equi convex,

R₁ = R and R₂ = -R and f = 1/P

⇒1/(1/P) = (μ - 1)[1/R - (-1/R)]

⇒P = 2(μ - 1)/R .........(1)

now after cutting in two halves, two plano convex lenses are created.

for a plano convex lens ,

R₁ = ∞ , R₂ = -R

⇒1/f' = (μ - 1)[1/∞ - (-1/R)]

⇒1/f' = (μ - 1)/R

from equation (1) we get,

⇒1/f' = (μ - 1)/[2(μ - 1)/P ] = P/2

⇒P' = P/2

Therefore the power of plano convex lens is P/2