To understand multislit interference and how it leads to the design of diffracti

Question

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 for constructive interference from a pair of slits are given by the equation dsin()=m, where d is the separation between the slits, is the wavelength of the light, and m is an integer.

Question

What is the angle ^2 to the second-order maximum from a diffraction grating with slits spacedd1 apart, for light of wavelength _1?

Express your answer in terms of _1 and d_1.

Explanation / Answer

the angle is calculated as follows:

d1Sinm = m1

For m = 2,

2 = Sin-1(21/d1)

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