Physics · Ch 6 — Optics
Dispersive Power
Dispersive Power
If are the deviations a prism produces for violet and red light, of refractive indices , then is called the angular dispersion -- the angular gap between the two extreme colours of the spectrum, depending on the prism's apex angle and on the material (through ). Taking as the deviation for a mean (middle) colour such as yellow or green, and as its corresponding refractive index, dispersive power is defined as , a dimensionless, always-positive quantity that depends only on the nature of the prism material, not on the size of its ape …
| Colour | Wavelength (nm) | Crown glass | Flint glass |
|---|---|---|---|
| Violet | 396.9 | 1.533 | 1.663 |
| Blue | 486.1 | 1.523 | 1.639 |
What this figure shows. A prism is shown splitting an incident beam into just its two extreme visible colours, violet and red, each deviated by its own angle, delta(V) for violet (the larger deviation) and delta(R) for red (the smaller deviation); the angular gap between these two deviated rays, delta(V) minus delta(R), is the angular dispersion produced by the prism, the quantity dispersive power is built from by dividing it by the deviation of a middle (mean) …
Worked out. Flint glass has refractive indices 1.632 for violet, 1.613 for red, and 1.620 for (mean) green light. Substituting into the dispersive-power formula omega = (nV - nR)/(nG - 1) gives omega = (1.632 - 1.613)/(1.620 - 1) = 0.019/0.620 = 0.0306. Because dispersive power is a dimensionless ratio, this value of about 0.031 characterises flint glass's colour-splitting ability on its own, independent of whatever particular apex angle a prism happens …