DISPERSION

Posted on

The phenomenon of splitting of light into its component colours is known as dispersion.

SPECTRUM: The pattern of colour components of light is called the spectrum.

ANGULAR DISPERSION: “The angle between the two rays corresponding to the extreme colours red and violet in the spectrum is called angular dispersion”.

\delta \, = \,{\delta _v}\, - \,{\delta _R}

DISPERSIVE POWER: The ratio of angular dispersion between the extreme colours to the deviation of mean ray (yellow) is called the dispersive power.

Dispersive power is the characteristic of the material of the prism and reflects the ability of a prism to disperse the light.

VARIATION OF REFRACTIVE INDEX WITH WAVELENGTH:

According to Cauchy’s formula

clip_image008

n\, = \,a\, + \,\frac{b}{{{\lambda ^2}}}\, + \,\,\frac{c}{{{\lambda ^4}}}

Where a, b and c are constants for the material.

n – Refractive index of a material for light of certain wavelength.

CAUSE OF DISPERSION:

clip_image011[4]

Since colour is associated with wavelength of light. In the visible spectrum VIBGYOR violet has least wavelength while red has maximum wavelength.

Since {\lambda _r}\, > \,{\lambda _{\rm{v}}}

\therefore \,\,\,\,\,\,\,\,\,\,{n_r}\,\,\, < \,\,\,{n_{\rm{v}}}

Since \delta \,\, = \,\left( {n\, - \,1} \right)\,A

\begin{array}{l} \therefore \,\,\,\,\,\,\,\,{\delta _{\rm{v}}}\, = \,\,\left( {{n_{\rm{v}}}\, - \,1} \right)\,A\\ \,\,\,\,\,\,\,\,\,{\delta _R}\, = \,\left( {{n_R}\, - \,1} \right)\,A \end{array}

\therefore \,\,\,\,\,\,\,\,\,\,\,{\delta _{\rm{v}}}\,\,\, > \,\,\,{\delta _R}

Thus violet colour deviate most while red colour deviate least.

SPEED OF COLOUR OF LIGHT:

V\, = \,\frac{C}{n}

Since n is different for different colour therefore speed varies with colour.

Since {n_{\,r}}\,\, < \,\,{n_V}

Therefore, red colour travel faster than violet.

Note: Since n is different for different colour therefore different colour deviate through different angles while passing through the prism and hence they are seen as separate.

DISPERSIVE MEDIUM:

A substance in which the speed of a light varies with wavelength shows dispersion. e.g Glass.

NON – DISPERSIVE MEDIUM:

In vacuum the speed of light is independent of wavelength due to which all colour travel with the same speed.

NEWTON’S EXPERIMENT:

Does the prism itself create colour in some way or does it only separate the colours already present in white light?

Isaac newton placed two prism but in an inverted portion.

image

The first prism splits the white light into its component colours, while the inverted prism recombines them to give white light.

Thus the prism separate the white light into its component colours.