DISPERSION OF THE LIGHT ON THE PRISM

Refraction index of any material depends upon the wavelength of the light. This fact can be used to resolve the light beam into the spectral components it consists of. One of the tools used for spectrum analysis of light is the glass prism.

Let us consider and beam of the light propagating symmetrically to prism (see the figure). If a is the refractive angle of the prism, then we can find from the condition n = sin x0 / sin x = sin z / sin z 0 that

n = sin (a/2 + j/2) / sin ( a/2 ) (1)

In practice the refraction index n depends upon the light wavelength

l , so the angle j at which the prism refracts the light will depend upon the light wavelength too:

D = d j / d l = (d j / dn)(dn / d l ) (2)

Value dn / d

l is called the dispersion of the material. This constant and refractive index n(l) characterize the basic optical properties of the material the prism is made of. Differentiating the formula (1) we can find the premultiplier in the equation (2). Really:

dn / d

j = cos (a /2 + j /2) / 2sin ( a /2 ) (3)

and therefore

(4)

We can see from this formula that to achieve the maximal resolution of the prism on the wavelength we should use the materials with the maximal values of refraction index n and dispersion constant (dn / d

l ).

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