What is diffraction grating and grating element? Explain the experimental method to determine the wavelength of the spectral line using diffraction grating?
1 Answer

Diffraction grating:

A diffraction grating is an arrangement consisting of a large number of parallel slits of same width and separated by equal opaque spacing. It is obtained by ruling equidistant parallel lines on a glass plate with the help of a fine diamond point.

Grating element:

Let N be the number of parallel slits, each of width 'a' and separated by opaque space 'b'. Then, the distance between the centers of the adjacent slits is $d = a + b$ and is known as grating element.

Determination of wavelength of the spectral line using diffraction grating:

The diffraction grating is often used in the Lab for the determination of wavelength of light. The grating spectrum of the given source of monochromatic light is obtained by using a spectrometer as shown -

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Symmetrical diffraction pattern consisting of different orders can be seen. The angle of diffraction $\theta$ for a particular order 'm' of the spectrum is measured.

The number of lines per inch of grating are written over it by the manufacturer. Hence the grating element is

$$ a + b = \frac{1}{ \text{No. of Lines / cm}} = \frac{2.54}{ \text{No. of Lines / inch} } $$

Thus, using equation $(a + b) sin \theta = m \lambda$

The unknown wavelength $'\lambda'$ of the spectral line can be calculated by putting the value of the grating element (a+b), the order 'm' and the angle of diffraction $'\theta'$

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