Explain the experimental method to determine the wavelength of spectral lines using grating. A diffraction grating has 5000 lines / cm and the total ruled with is 5cm. Calculate dispersion for a wavelength of 5000 A0 in the second order.

#### Solution

1. The grating spectrum of the given source of monochromatic light is obtained by using a spectrometer.

2. The spectrometer is first adjusted for parallel rays. The grating is then placed on the prism table and adjusted for normal incidence.

3. In the same direction as that of the incident light, the direct image of the slit or the zero order spectrum can be seen in the telescope.

4. On either side of this direct image a symmetrical diffraction θ for a particular order m of the spectrum is measured.

5. The number of the lines per inch of grating are written it by manufacturers.

`( a+ b ) =1/"number of lines /cm" = 2.54/"number of lines /inch"`

(a+b)sinθ = mλ

The unknown wavelength λ can be calculated by putting values of grating

element (a+b), the order m, and angle of diffraction θ.

`(a+b) = 1/5000`

n = 2

using grating equation

nλ =(a+b)sinθ

`2xx5000xx10^(-8) = 1/5000 xxsin θ`

Cosθ = 0.866

Now dispersion power

`d (d theta)/(dλ) = n/((a+b)cos theta ) = 2/(1/5000+0.866`

= 11547