Question

Why central rings in the Newton's ring always be dark.

Answer 1

Answer on Question #65379, Physics / Optics

Why central rings in the Newton's ring always be dark.

Solution:

Optical path difference of waves 1 and 2:

$$\mathrm {O P D} = \mathrm {n d} + \frac {\lambda}{2} (1),$$

where $n$ is refractive index of layer (air), $d$ is physical length, $\lambda$ is wavelength.

Light passes from medium with less optical density (air) to the medium with more optical density (glass). In this way, OPD increases by $\frac{\lambda}{2}$ .

For central ring: $d = 0$ m (2).

(2) in (1): $\mathrm{OPD} = \frac{\lambda}{2}$ (3)

The condition of minimum interference (dark rings):

$$\mathrm {O P D} = (2 k + 1) \frac {\lambda}{2} (4),$$

where $k = 0, \pm 1, \pm 2, \ldots$

Of (4) $\Rightarrow$ if $k = 0$ , then $\mathrm{OPD} = \frac{\lambda}{2}$ (5)

Of (3) and (5) $\Rightarrow$ central rings in the Newton's rings always be dark.

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