Total reflection may be thus simply illustrated:—­Place a shilling in a drinking-glass, and tilt the glass so that the light from the shilling shall fall with the necessary obliquity upon the water surface above it.  Look upwards through the water towards that surface, and you see the image of the shilling shining there as brightly as the shilling itself.  Thrust the closed end of an empty test-tube into water, and incline the tube.  When the inclination is sufficient, horizontal light falling upon the tube cannot enter the air within it, but is totally reflected upward:  when looked down upon, such a tube looks quite as bright as burnished silver.  Pour a little water into the tube; as the liquid rises, total reflection is abolished, and with it the lustre, leaving a gradually diminishing shining zone, which disappears wholly when the level of the water within the tube reaches that without it.  Any glass tube, with its end stopped water-tight, will produce this effect, which is both beautiful and instructive.

Total reflection never occurs except in the attempted passage of a ray from a more refracting to a less refracting medium; but in this case, when the obliquity is sufficient, it always occurs.  The mirage of the desert, and other phantasmal appearances in the atmosphere, are in part due to it.  When, for example, the sun heats an expanse of sand, the layer of air in contact with the sand becomes lighter and less refracting than the air above it:  consequently, the rays from a distant object, striking very obliquely on the surface of the heated stratum, are sometimes totally reflected upwards, thus producing images similar to those produced by water.  I have seen the image of a rock called Mont Tombeline distinctly reflected from the heated air of the strand of Normandy near Avranches; and by such delusive appearances the thirsty soldiers of the French army in Egypt were greatly tantalised.

The angle which marks the limit beyond which total reflection takes place is called the limiting angle (it is marked in fig. 6 by the strong line E n’’).  It must evidently diminish as the refractive index increases.  For water it is 481/2 deg., for flint glass 38 deg.41’, and for diamond 23 deg.42’.  Thus all the light incident from two complete quadrants, or 180 deg., in the case of diamond, is condensed into an angular space of 47 deg.22’ (twice 23 deg.42’) by refraction.  Coupled with its great refraction, are the great dispersive and great reflective powers of diamond; hence the extraordinary radiance of the gem, both as regards white light and prismatic light.

Sec. 5. Velocity of Light.  Aberration.  Principle of least Action.