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Lens Maker Formula

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Lens maker formula is an expression that shows relation between the refractive index, the focal length and the radii of curvatures of the lens.

1f = (n1)(1R1 + 1R2)

where,

f = focal length of the lens

n = refractive index of the lens

R1 ,R2 = radii of curvatures of the lens

Assumptions:

1. The lens is thin

2. deviation produced by the thin lens is similar to that of a small angle prism

3. angle made by incident ray and refracted ray with principle axis is small

:

from fig:

In  ΔXOF,

tanδ = OX/OF

or, tanδ = h/f

for small angle tanδ ≈ δ

.˙. δ = h/f.............:1

we know,

δ = A(n-1)............:2

from equations 1 and 2

h/f =A(n-1)............:3




from geometry,

angle MXG = A

or, A = a+a'

or, A = h/R1 + h/R2

or A =h(1/R1 + 1/R2).............:4

now, from equation 3

or, h/f = h(n-1)(1/R1 + 1/R2)

1/f = (n-1)(1/R1 + 1/R2)