Question

Why is the central fringe is dark?

Answer 1

Newton Ring Experiment:

Diagram:

1. In the Newton ring experiment, a glass plate (G) and a thin plano-convex lens(C) of a large radius are inclined at an angle of $45°$ with horizontal plane.
2. When a monochromatic comes from a sodium lamp and by reflection from glass plate(G) falls normally on the plano-convex lens (C) and glass plate (P) below it.
3. The rays of light after passing through the thin lens become parallel and strike the glass plate which is partially silvered.
4. These rays get reflected and strike the plano-convex lens.
5. The air film is formed between the flat glass plate and the lower face of the plano-convex lens.
6. The air film is formed circular and its width varies from zero to infinity.
7. The light rays reflected from the upper surface of the glass plate and the lower surface of the plano-convex lens has some path difference.
8. These reflected rays get superimposed and form an interference pattern in the form of a ring called Newton’s ring.
9. The central ring is dark and then alternate dark and bright rings are formed as shown in the figure alongside.
10. These rings are formed due to the superposition of the reflected beam of light.

Explanation:

Path difference in Newton's Ring Experiment is given by:

$∆x=2t+\frac{\lambda }{2}$

Where, $∆x$ = path difference, $t$= thickness of air film, $\lambda$ = wavelength of light used.

In the case of the central ring where $t=0$,

$∆x=\frac{\lambda }{2}$

Since path difference $\frac{\lambda }{2}$ is a condition of destructive interference.

Thus central fringe is dark in Newton's Ring Experiment.