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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?

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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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