Advanced Physics Topics like quantum mechanics and relativity have revolutionized our understanding of the universe.
On What Factors Does Dispersive Power Depend?
Colour may be defined as the visual sensation produced by a particular wavelength. Radiations of numerous wavelengths are emitted from white light. Visible radiations are limited within a definite range of wavelength, from 4000 A to 8000 A. This range is called visible range of spectrum or visible spectrum. The approximate wavelengths of seven elementary colours of visible spectrum are given below in angstrom (A) unit. (1 A = 10-10 m)
The sensitivity of the eye is different for different colours. A nor-mal human eye is most sensitive to yellow region in a visible spectrum. Sensitivity to other colours situated on either side of the yellow region gradually diminishes.
Angular Dispersion and Dispersive Power
Deviation in a thin prism of refracting angle A is given by
δ = (µ – 1)A
When a ray of white light passes through the prism, it splits up into its constituent colours. The deviation of the mean ray,
δ = (µ – 1)A ……. (1)
Let µr and µv be the refractive indices of the prism for red and violet rays and δr and δv be the corresponding deviations.
So, δr = (µr – 1)A ….. (2)
δv = (µv – 1)A ….. (3)
δv – δr = (µv – µr)A ….. (4)
This difference (δv – δr) is called angular dispersion for the two colours.
Now, δv – δr = (µv – µr)A = \(\frac{\mu_v-\mu_r}{\mu-1}\) × (µ – 1)A
= \(\frac{\mu_v-\mu_r}{\mu-1}\) × δ [using equation (1)] …. (5)
So, \(\frac{\delta_v-\delta_r}{\delta}\) = \(\frac{\mu_v-\mu_r}{\mu-1}\) = ω ….. (6)
[ω = dispersive power of the refracting medium]
Thus, δv – δr = ωδ
Dispersive power depends on the nature of the medium. It is a unitless and dimensionless quantity.
Definition : The dispersive power of a medium is defined as the angular dispersion for violet and red rays per unit deviation of the mean ray in the medium.
From equation (6) we get.
ω = \(\frac{\mu_\nu-\mu_r}{\mu-1}\) = \(\frac{d \mu}{\mu-1}\) [µv – µr = dµ]
Angular dispersion,
δv – δr = ω × δ
= dispersive power × deviation of middle ray
1. Dispersive power of flint glass is greater than that for crown glass.
2. Dispersive power of any material medium is always positive (since µv > µ<sub.r, and µ > 1).