Question

c) Discuss the concept of missing orders with reference to double slit diffraction
pattern.

Answer 1

Answer on Question #69270, Physics / Optics

c) Discuss the concept of missing orders with reference to double slit diffraction pattern.

Solution:

It is Fraunhofer diffraction by two slits.

A missing order occurs when the "diffraction minimum" overlaps with the "interference maximum".

Analytical expression for diffraction by two slits:

$\mathrm{I}(\theta) = \mathrm{I}(0)\left(\frac{\sin\beta}{\beta}\right)^2\cos^2\alpha (1),$ where $\mathrm{I}$ is the intensity of diffracted light, $\alpha = (\pi a / \lambda)\sin \theta$, $\beta = (\pi b / \lambda)\sin \theta$, $\mathrm{b}$ is the slit width, $\mathrm{a}$ is the slit separation, $\lambda$ is the wavelength of light

Zeros: $\beta = \pm \pi, \pm 2\pi, \pm 3\pi \ldots$

$$\alpha = \pm \pi / 2, \pm 3 \pi / 2, \pm 5 \pi / 2 \dots$$

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