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Plane diffraction grating

An arrangement consisting of a large number of parallel slits of same width and separated by equal opaque spaces is called diffraction grating. If a is width of each slit and b is width of each opaque space, then (a + b) is called grating element.

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Theory of diffraction grating (normal incidence)

Consider parallel beam of light striking the transmission diffraction grating MN.
The waves from different slits superpose and produce diffraction pattern on the screen. The pattern consists of a number of principal maxima with minima and secondary maxima in between.
The incident beam travelling in the same direction will be brought to focus at O which corresponds to central maximum.

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Diffraction Grating

To find the intensity at 𝑃1 - Fraunhofer diffraction at a single slit is applied. The wavelet travelling from all the points in a slit along the direction 𝜃 are equivalent to a single wave of amplitude

If there are N slits, there are N waves each from middle of the slits. The path difference between any two consecutive slits is

In triangle ACG, CG is the path difference and

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Diffraction Grating

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Diffraction Grating

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Diffraction Grating

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Diffraction Grating

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Diffraction Grating

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Theory of diffraction grating (oblique incidence)

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Theory of diffraction grating

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Determination of wavelength of spectral line using diffraction grating

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Dispersive power of grating

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Resolving power

The ability of an optical instrument to show two close lying point objects, as well separated point objects is called its resolving power. The resolution is limited by the diffraction patterns of the two close lying point objects which overlap as shown.

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Rayleigh criterion for resolution

Condition for just resolved – Two close lying sources of light or point objects are said to be just resolved, if the central maximum of the diffraction pattern due to one source coincides with the first minimum of the diffraction pattern due to the second source. It also means that the distance between two central maxima due to two sources is equal to the distance between the central maximum and first minimum of any one of them.
Condition for well resolved – Two close lying sources of light or point objects are said to be well resolved, if the distance between two central maxima of the diffraction pattern due to two sources is greater than the distance between the central maximum and first minimum of any one of them.
Condition for unresolved – Two close lying sources of light or point objects are said to be unresolved, if the distance between two central maxima of the diffraction pattern due to two sources is less than the distance between the central maximum and first minimum of any one of them.

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Resolving power of grating

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Resolving power of grating

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Resolving power of a telescope

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Differences between dispersive power and resolving power of grating

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Differences between Prism spectrum and Grating spectrum

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Difference between Interference and Diffraction

S.No.	Interference	Diffraction
1.	It is the modification in the intensity of light due to super position of two or more light waves.	It is the bending of light around the corners of small obstacles and hence it's spreading into the region of geometrical shadow
2.	It is due to the superposition of finite number of waves from different coherent sources.	It is due to the superposition of infinite number of secondary waves from different points of the same wave-front
3.	Interference fringes are of equal width.	Diffraction fringes are of unequal width. The width of the central band is maximum and the widths of the less bright bands gradually decrease.
4.	Interference pattern consists of alternately bright and dark bands, all the bright bands being of the same brightness.	Diffraction pattern consists of a central bright band of maximum brightness, surrounded on either side by alternately dark and less bright bands called secondary maxima.