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Fundamentals Of Physics
Found in: Page 1115

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Short Answer

Show that the dispersion of a grating is D=tanθλ

It is proved that the dispersion of a grating is tanθλ

See the step by step solution

Step by Step Solution

Step 1: Definition and concept of diffraction from a grating

An optical element with a periodic structure that divides light into a number of beams that move in diverse directions is known as a diffraction grating.

The angular distance θof the mthorder diffraction pattern produced from a grating having line separation is

dsinθ=mλ …(i)

Here, λ is the wavelength of the incident light.

Step 2: Showing that dispersion of a grating  D=tanθλ

The dispersion is given by


Differentiate equation (i) with respect to λ to get


Substitute form of m from equation (i) to get


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