Question

At the crest of a spherical surface of a plano-convex lens there is a ground-off plane spot of radius `r_(0) = 3.0mm` through which the lens comes into contact with a glass plate. The curvature radius of the sixth bright ring when observed in reflected light with wavelength `lambda = 655 nm`.

Answer 1

In this case the path difference is `(r^(2) - r_(0)^(2))/(R )` for `r gt r_(0)` and zero for `r le r_(0)`.
This must equals `(k - 1//2) lambda` (where `k = 6` for the `six^(th)` bright ring.)
Thus `r = sqrt(r_(0)^(2) + (k - (1)/(2)) lambdaR) = 3.8 mm`