ART. 143 - On the Existence of Reflection when the Relative Refractive Index is Unity

Summary

The copious undisturbed transmission of light by glass powder when surrounded by liquid of the same index, as in Christiansen's experiment [vol. II. p. 433], suggests the question whether the reflection of any particular ray is really annihilated when the relative refractive index is unity for that ray. Such would be the case according to Fresnel's formulæ, but these are known to be in some respects imperfect. Mechanical theory would indicate that when there is dispersion, reflection would cease to be merely a function of the index or ratio of wave-velocities. We may imagine a stretched string vibrating transversely under the influence of tension, and in a subordinate degree of stiffness, to be composed of two parts so related to one another in respect of mass and stiffness that the wave-velocity is the same in both parts for a specified wave-length. But, as it is easy to see, this adjustment will not secure the complete transmission of a train of progressive waves incident upon the junction, even when the wave-length is precisely that for which the velocities are the same.

The experiments that I have tried have been upon plate glass immersed in a mixture of bisulphide of carbon and benzole, of which the first is more refractive and the second less refractive than the glass; and it was found that the reflection of a candle-flame from a carefully cleaned plate remained pretty strong at moderate angles of incidence, in whatever proportions the liquids were mixed.