Question

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.​

Answer 1

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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