Explain the experimental method to determine the wavelength of spectral line using diffraction grating.

What is the highest order spectrum which can be seen with monochromatic light of wavelength 6000 A^{o} by means of a diffraction grating with 5000 lines/cm?

#### Solution

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

** 2.**The arrangement is as shown in Figure shown below.

** 3**.The spectrometer is first adjusted for parallel rays.

** 4**.The grating is then placed on the prism table and adjusted for normal incidence.

**5**.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.

**6**.On either side of this direct image a symmetrical diffraction pattern consisting of different orders can be seen.

** 7**.The angle of diffraction θ for a particular order m of the spectrum is measured.

**8**.Thus using the equation** (a + b) sin θ = mλ **the unknown wavelength λ can be calculated by putting the values of the grating element (a + b), the order m and the angle of diffraction θ.

9. The diffraction grating is often used in the laboratories for the determination of wavelength of light.

**Solution of problem** :

`N = 5000 ("lines")/(cm)`

`a + b = 1/5000 cm`

`"Using equation (a + b)sin θ = mλ"`

For m to be maximum sin θ should be equal to 1

`n = (a+b)/λ `

`= 1/(5000 xx 6000 xx 10^(−8) )`

= 3.3

**Maximum order of spectrum = 3 **