Physics · Chapter 18
Study notes aligned to the official NEB syllabus.
Dispersion of light is the phenomenon of splitting of white light into its constituent colours when it passes through a refracting medium such as a glass prism. The band of colours so produced, in the order violet, indigo, blue, green, yellow, orange, red (remembered by the word VIBGYOR), is called the spectrum.
White light is a mixture of seven colours, each of a different wavelength. When such light enters a prism, refraction bends every colour, but the amount of bending is not the same for all colours because the refractive index of the glass depends on the wavelength of light. This variation of refractive index with wavelength is the true cause of dispersion.
Cause of dispersion. The refractive index $\mu$ of a transparent medium is larger for shorter wavelengths and smaller for longer wavelengths. Hence:
$$\mu_{\text{violet}} > \mu_{\text{red}}$$
Since the deviation produced by a prism increases with refractive index, violet light (shortest wavelength) is deviated the most and red light (longest wavelength) is deviated the least:
$$\delta_{\text{violet}} > \delta_{\text{red}}$$
This is why the emerging colours fan out into a spectrum. For a thin (small angled) prism of refracting angle $A$, the deviation of any colour of refractive index $\mu$ is:
$$\delta = A(\mu - 1)$$
The angular dispersion between any two colours is defined as the difference between the angles of deviation produced by the prism for those two colours.
Taking the two extreme colours of the visible spectrum, violet and red, for a thin prism of refracting angle $A$:
$$ \begin{aligned} \delta_v &= A(\mu_v - 1) \ \qquad \delta_r &= A(\mu_r - 1) \end{aligned} $$
where $\mu_v$ and $\mu_r$ are the refractive indices for violet and red light. The angular dispersion between violet and red is:
$$ \begin{aligned} \delta_v - \delta_r &= A(\mu_v - 1) - A(\mu_r - 1) \ \boxed{\delta_v - \delta_r = A(\mu_v - \mu_r)} \end{aligned} $$
Thus the angular dispersion depends on the refracting angle $A$ of the prism and on the difference $(\mu_v - \mu_r)$ of the refractive indices, which is a property of the material of the prism.
(covers learning outcome 18.1)
A pure spectrum is one in which the constituent colours are completely separated, so that each region of the spectrum contains light of one single colour (one wavelength) only, with no overlapping of adjacent colours.
In contrast, an impure spectrum is one in which the colours overlap one another, so that no part of the spectrum is due to a single wavelength alone. The ordinary spectrum obtained by simply passing a narrow beam of white light through a prism and receiving it on a screen is impure, because each point of the source sends out an independent cone of coloured light and these cones overlap on the screen.
Conditions required to obtain a pure spectrum. To make the spectrum pure, the light of each single wavelength must be brought to a separate, sharp position. This requires the following arrangement:
The lenses used are made achromatic (free from chromatic aberration, see Section 6) so that they do not themselves introduce colour errors. With this arrangement each colour occupies its own distinct position and the spectrum obtained is pure.
Dispersion of light is the phenomenon of splitting of white light into its constituent colours when it passes through a refracting medium such as a glass prism. The band of colours so produced, in the order violet, indigo, blue, green, yellow, orange, red (remembered by the word VIBGYOR), is called the spectrum.
White light is a mixture of seven colours, each of a different wavelength. When such light enters a prism, refraction bends every colour, but the amount of bending is not the same for all colours because the refractive index of the glass depends on the wavelength of light. This variation of refractive index with wavelength is the true cause of dispersion.
Cause of dispersion. The refractive index of a transparent medium is larger for shorter wavelengths and smaller for longer wavelengths. Hence:
Since the deviation produced by a prism increases with refractive index, violet light (shortest wavelength) is deviated the most and red light (longest wavelength) is deviated the least:
This is why the emerging colours fan out into a spectrum. For a thin (small angled) prism of refracting angle , the deviation of any colour of refractive index is:
The angular dispersion between any two colours is defined as the difference between the angles of deviation produced by the prism for those two colours.
Taking the two extreme colours of the visible spectrum, violet and red, for a thin prism of refracting angle :
where and are the refractive indices for violet and red light. The angular dispersion between violet and red is:
Thus the angular dispersion depends on the refracting angle of the prism and on the difference of the refractive indices, which is a property of the material of the prism.
(covers learning outcome 18.1)
A pure spectrum is one in which the constituent colours are completely separated, so that each region of the spectrum contains light of one single colour (one wavelength) only, with no overlapping of adjacent colours.
In contrast, an impure spectrum is one in which the colours overlap one another, so that no part of the spectrum is due to a single wavelength alone. The ordinary spectrum obtained by simply passing a narrow beam of white light through a prism and receiving it on a screen is impure, because each point of the source sends out an independent cone of coloured light and these cones overlap on the screen.
Conditions required to obtain a pure spectrum. To make the spectrum pure, the light of each single wavelength must be brought to a separate, sharp position. This requires the following arrangement:
The lenses used are made achromatic (free from chromatic aberration, see Section 6) so that they do not themselves introduce colour errors. With this arrangement each colour occupies its own distinct position and the spectrum obtained is pure.