1. In Newton's ring experiment, sodium light is used (A1=589 nm, 12=589.6nm). Radius of curvature of plano-convex lens R=100 nm.
Calculate the order number of the ring at which they fades away. Find out the distance from the point of contact from where the rings fades away.
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Thus the distance from the point of contact is 17 mm.
Explanation:
Given data:
Radius of curvature of plano-convex lens = 100 cm
Sharpness of the rings pattern is the worst when the maxima and minima intermingle.
For the maxima
r^2 = 2 Rλ (2 k − 1)
For the minima
r^2 = kλR
So,
kλ 1 R = Rλ2 (2.k − 1) / 2
→ kλ 1 = λ2 (2.k − 1) / 2
λ1 = λ
λ2 = λ1 + Δλ = λ + Δλ
kλ= (λ+Δλ)(2k−1) / 2
kΔλ ≈ λ / 2
k = λ / 2Δλ = λ 1 / 2(λ 2 −λ 1 ) = 589 / 2(589.6−589) ≈ 491
l = √ R^ 2 − (R − kλ / 2)^ 2
l = 1^2 − (1 − 491⋅589⋅10^−9 / 2 )^2
l ≈ 0.017 m = 17 mm
Thus the distance from the point of contact is 17 mm.
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