In the Newton's Ring Experiment why is the central fringe a light fringe? Why does constructive interference happen at the center?

Does it have anything to do with the sense of thickness between point of contact of the lens and surface?


The $m_{th}$ order interference minima will satisfy the relation

$$ 2n_fd_{m} = m\lambda_f, \quad m = 0, 1, 2, \dots $$

where, $d_{m}$ is the thickness of the air film between the convex lens and the optical flat lens.
Radius of the $m_{th}$ dark ring is given by

$$ x_m = \sqrt{m\lambda_{f}R}, \quad m = 0, 1, 2, \dots $$

It's obvious from the above two equations, if the convex lens and flat lens have good contact (no dust), the central fringe at the point of contact ($x_0 = 0$) will be minima since, $d$ goes to zero at that point.


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