Derive the Fraunhofer pattern for an array of N slits and show that it gives the familiar result for double slits when N = 2. Hints: Choose coordinates so that the slits are centred at x = 0, a, 2a, ... and stay in complex notation for as long as possible.

Derive the Fraunhofer pattern for an array of N slits and show that it gives the familiar result for double slits when N = 2. Hints: Choose coordinates so that the slits are centred at x = 0, a, 2a, ... and stay in complex notation for as long as possible.

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter4: Diffraction

Section: Chapter Questions

Problem 5CQ: In our study of diffraction by a single slit, we assume that the length of the slit is much larger...

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Concept explainers

Interference of Light

The word "constructive" signifies addition in interference. Constructive interference occurs when the path of the waves that start from the slit differs by 1 entire wavelength or in the intervals of the same. Hence, the waves that are presented on the screen are in phase (crest to crest/trough to trough). The waves interfering constructively forms bright fringes on the screen.

Question

Derive the Fraunhofer pattern for an array of N slits and show that it gives the familiar result for
double slits when N = 2.
Hints: Choose coordinates so that the slits are centred at x = 0, a, 2a, ... and stay in complex
notation for as long as possible.

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