In a two-beam interferometer the orange mercury line composed of two wavelengths `lambda_(1) = 576.97 nm` and `lambda_(2) = 579.03 nm` is employed. What is the least order of interference at which the sharpness of the fringe pattern is the worst ?

Explanation

Sharpness of the fringe pattem is the worst when the maxima and minima intermingle:
`n_(1) lambda_(1) = (n_(1) - (1)/(2))lambda_(2)`
or putting `lambda_(1) = lambda, lambda_(2) = lambda + Delta lambda`
we get `n_(1) Delta lambda = (lambda)/(2)`
or `n_(1) = (lambda)/(2Delta lambda) = (lambda_(1))/(2(lambda_(2) - lambda_(1))) = 140`