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Prism Resolving Power

The term resolving power is applied to spectrographic devices using a prism or a grating. Resolving power signifies the ability of the instrument to form separate spectral images of two neighbouring wavelengths, λ and λ + dλ in the wavelength region λ.

In fig. S is a source of light, L₁ is a collimating lens and L₂ is the telescope objective. As the two wavelengths λ and λ + dλ are very close, if the prism is set in the minimum deviation position it would hold good for both the wavelengths. The final image I₁ corresponds to the principal maximum for wavelength λ and image I₂ corresponds to the principal maximum for wavelength, λ + dλ. I₁ and I₂ are formed at the focal plane of the telescope objective L₂. The face of the prism limits the incident beam to a rectangular section of width a. Hence, the Rayleigh criterion can be applied in the case of a rectangular aperture.

In the case of diffraction at a rectangular aperture, the position of I₂ will correspond to the first minimum of the image I₁ for wavelength λ₁ provided

a.dδ = λ

or, dδ = λ/a (i)

Here, δ is the angle of minimum deviation for wavelength λ.

From the figure,

+ A + + δ = π

In the case of a prism

Here and δ are dependent on wavelength of light λ.

Differentiating equation (iv) with respect to

Substituting the values from equations (ii) and (iii),

Substituting the value of dδ from equation (i),

The expression λ/dλ measures the resolving power of the prism. It is defined as the ratio of the wavelength of a spectral line to the difference in wavelength between the line and a neighbouring line such that the two lines appear just resolved, according to Rayleigh’s criterion.

Thus, the resolving power of a prism is (i) directly proportional to the length of the base and (ii) rate of change of refractive index with respect to wavelength for that particular material. The expression for resolving power given above is applicable only to spectral lines of equal intensity. If two spectral lines are of different intensities then the value of dλ i.e. the difference in wavelength between the two lines must be higher so that the two lines appear as separate ones.