Dispersion and Spectrometer

Dispersion

When a beam of white light is made to fall on one refracting face of the prism, it splits into seven colours i.e. violet, indigo, blue, green, yellow, orange and red from base. The phenomenon of the splitting of white light into its constituent colours is called dispersion of light.

Cause of dispersion

The colour of light depends on upon its wavelength. The red colour in visible light has maximum wavelength and violet colour the minimum wavelength. Cauchy has derived a relation between refractive index and wavelength as
$$ \mu = a + \frac {b}{\lambda ^2} + \frac {c}{\lambda ^4} $$

where a, b and c are constant for the materials of the prism. We know for small angle of deviation, \(\delta = A(\mu – 1) \). Since wave length of violet light is smaller than that of red light, refractive index \( \mu _v > \mu _r \). So, on entering the prism, the violet light is refracted through larger angle than red light, so \(\delta _v > \delta _r \). Thus, when while light is incident on the first face of the prism, each colour is refracted through different angles, i.e angle of refraction is maximum for a red light and least for violet. As a result, dispersion takes place.

The Spectrometer

A spectrometer is an optical device used to produce the spectrum of light from a source and to measure the refractive index of the material in the form of prism for different colours. A spectrometer essentially consists of three components: collimator, prism table and telescope as shown in figure.

Collimator:

It consists of a tube of variable length with an adjustable slit slits S at one end and convex lens L₁ at the other. When a source of light is placed close to S, a parallel beam of light will emerge.

Prism table:

It has a horizontal circular base for keeping prism and can be rotated about a vertical axis passing through its centre. The position of table can be read with the help of two veneers V₁ and V₂.

Telescope:
An astronomical telescope is used to observe the spectrum emerging from the prism. The distance between eye-piece and objective can be changed by using rack and pinion arrangement. A piece of cross-wire is kept in front of the eye-piece.

Adjustment

In the spectrometer, three components are fitted in one compact form. The prism table and the telescope can be rotated about a vertical axis passing through the centre of prism table. The angle of rotation of the telescope can be measured with the help of circular scale and the vernier scales V₁ and V₂ on the table. The axis of the collimator, telescope and prism table are made horizontal with the help levelling screw. The light source which is to be examined is placed behind the slit of the collimator. The distance between the slit and lens in the collimator is so adjusted that the slit lies in the focus of the lens and the rays coming out of the collimator become parallel. This parallel beam is made incident on the prism on the horizontal table which dispersed the light beam. The dispersed beam is received by the telescope which is focused on the dispersed beam. The telescope is rotated and light rays of different wavelengths or colours are received at various angular positions of the telescope.

Pure and Impure Spectrum

When a ray of white light is incident on a prism, the light is split into different constituent colours and deviated through different angles. Such dispersed light is received on a screen or a photographic plate. A collection of dispersed light which gives its wavelength composition is called the spectrum. If the split rays overlap to each other, all colours can’t be seen distinctly on the screen. Such spectrum is called impure spectrum which is shown in figure.

However, if the spectrum on the screen in which the split colours don’t overlap to each other, all colours can be seen distinctly and it is called the pure spectrum. A pure spectrum can be obtained by various-ways. A convex lens is introduced into the path of emergent rays which focus the rays on the screen forming a pure spectrum. It may be pointed out that it would be necessary to arrange the prism in minimum deviation otherwise the spectrum will be impure.