Answer: The rings are circular because each fringe is a locus of points of equal air-film thickness, and such points lie on circles centred at the point of contact. The centre is dark in reflected light because the film thickness there is zero and the extra phase change of \(\pi\) on reflection makes the path difference \(\lambda/2\), giving destructive interference.
Why the rings are circular:
- In Newton's rings, a thin air film is formed between a plano-convex lens and a plane glass plate. Its thickness is zero at the point of contact and increases outwards.
- Each fringe is the locus of points where the film has the same thickness (fringes of equal thickness).
- Because the lens surface is spherical, points of equal air-film thickness lie on circles with the point of contact as centre. Hence the fringes are concentric circles. (For a wedge-shaped film, points of equal thickness lie on straight lines parallel to the edge, so those fringes are straight.)
Why the centre is dark (reflected light):
- For reflected light, the effective path difference between the two interfering rays is \(\Delta=2\mu t\cos r+\frac{\lambda}{2}\). The extra \(\frac{\lambda}{2}\) arises because the ray reflected from the lower surface of the air film (at the denser glass plate) suffers a phase change of \(\pi\).
- At the point of contact \(t=0\), so \(\Delta=\frac{\lambda}{2}\).
- A path difference of \(\frac{\lambda}{2}\) is the condition for destructive interference, so the centre of the reflected pattern is dark.