Learning Goal: To understand multislit interference and how it leads to the desi

Question

Learning Goal: To understand multislit interference and how it leads to the design of diffraction gratings.
Diffraction gratings are used in modern spectrometers to separate the wavelengths of visible light. The working of a diffraction grating may be understood through multislit interference, which can be understood as an extension of two-slit interference. In this problem, you will follow the progression from two-slit to many-slit interference to arrive at the important equations describing diffraction gratings.
A typical diffraction grating consists of a thin, opaque object with a series of very closely spaced slits in it. (There are also reflection gratings, which use a mirror with nonreflecting lines etched into it to provide the same effects.) To see how a diffraction grating can separate different wavelengths within a spectrum, we will first consider a "grating" with only two slits.
Recall that the angles THETA for constructive interference from a pair of slits are given by the equation dsin(theta)=m*lambda, where d is the separation between the slits,

Explanation / Answer

A link to the full solution for reference: https://notendur.hi.is/eme1/skoli/edl_v06/mp/36/Multislit%20Interference%20and%20Diffraction%20Gratings.htm

(This link also appears on Google if you enter the first paragraph of the problem statement if you don't trust me.)

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