R=100cm
Sharpness of the rings pattern is the worst when the maxima and minima intermingle.
For the maxima
r2=2Rλ(2k−1)
For the minima
r2=kλR
So,
kλ1R=2Rλ2(2k−1)→kλ1=2λ2(2k−1) , λ1=λ,λ2=λ1+Δλ=λ+Δλ
kλ=2(λ+Δλ)(2k−1)→kΔλ≈2λ
k=2Δλλ=2(λ2−λ1)λ1=2(589.6−589)589≈491
l=R2−(R−2kλ)2=12−(1−2491⋅589⋅10−9)2≈0.017m=17mm
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