# Principles of operation of optical methods

Optical methods allow the detection of density variations that occur in a fluid due to changes in temperature and/or speed and/or composition. The principle on which these methods are based is that the variation of density, p, produces a variation of the refractive index, n, of the fluid which in turn influences the trajectory (refraction) and the phase of the light rays that pass through the fluid. Appropriate optical devices convert the resulting effect in changes of light intensity on a screen or on a photograph.   The index of refraction, n, of a transparent medium, which is the ratio between the speed of light in vacuum and the speed of light in the substance, is related to the density by the Lorenz-Lorentz equation:

where R (l) is, for each substance, a function of the wavelength, l of the light.

When the index of refraction n = 1, as in the case of gases (see Table 6.1), Equation (6.1) can be expanded in series and, stopping the

 Substance Index of Refraction, n [-] (Sodium D line) Quartz 1.45843 Gelatin 1.516-1.534 Canada balsam 1.53 Crown Glass 1.517 Flint Glass 1.575-1.89 Water (15°C) 1.33377 Air (0°C, 760 mm Hg) 1.0002926 Carbon dioxide 1.000448-1.000454 Helium 1.00036-1.00036 Nitrogen 1.000296-1.000298 Water vapor 1.00249
 Table 6.1

 Refractive index of some substances

series at the first two terms, the simpler Gladstone-Dale equation is obtained:

n = 1 + K(X) p = 1 + ^( ) p (6.2)

Ps

where K(l) = 1.5 R(l) and ps is the density at standard conditions (T = 0°C, p = 760 mmHg).

The values of P for some gases are reported in Table 6.2.

Changes in the Gladstone-Dale constant with the wavelength are limited to a few percentages (see Table 6.3).

 Gas P.104 Air 2.92 Carbon dioxide 4.51 Nitrogen 2.97 Helium 0.36 Oxygen 2.71 Water vapor 2:54
 Table 6.2

 Values of constant P for l = 589.3 nm

 Wavelength l nm Gladstone-Dale constant K.103 m3kg_1 262.0 0.2426 296.0 0.2380 334.0 0.2348 436.0 0.2297 470.0 0.2287 479.8 0.2284 489.0 0.2281 505.0 0.2276 510.0 0.2276 521.0 0.2272 546.0 0.2269 578.0 0.2265 579.0 0.2263 614.7 0.2261 644.0 0.2258
 Table 6.3  