City of Light: The Story of Fiber Optics

26 CITY OF LIGHT
into glass bend into the glass, while light going from glass into air bends toward
the surface.
As light in the glass hits the surface at a steeper angle, it emerges into air
almost parallel to the surface. Eventually, it reaches a ‘‘critical angle’’ where it
cannot emerge into the air, as shown in figure B. (This critical angle is measured
from a line called the ‘‘normal’’ which is perpendicular to the surface.) All the
light outside the critical angle is reflected back into the glass. A For glass with a
refractive index of 1.5 in air, this angle is about 42 degrees. The higher the
refractive index, the larger the angle and the easier it is to see reflections
sparkling from within the glass.
Diamond has a refractive index of 2.4, so the critical angle is 25 degrees,
and much more light entering it undergoes total internal reflection as shown in
figure C. Diamond cutters take advantage of this effect and cleave the gems so
they collect light entering the top facet and reflect it back to the eye, making
them appear to shine. Because the refractive index changes with wavelength,
colors return at slightly different angles, making the stone glitter with color. B
(Zircon crystals have a refractive index of 2.1, so they glitter more than glass,
but not as brightly as diamond.) The variation of refractive index with wavelength
also breaks light passing through a prism into a spectrum and forms a rainbow
when sunlight strikes tiny water droplets. C
You can’t see total internal reflection in a window pane; you can only see it
in a large block of glass when you look at a surface at less than the critical
angle. Turn it in your hands and you can see total internal reflection start and
stop as you pass through the right angle. Fine crystal glass has a higher refractive
index than normal glass, so it shows total internal reflection more easily.
If you shine light along a glass rod or a jet of water, total internal reflection
will keep it within the glass or liquid. This light-guiding effect is the basis of fiber
optics.
A. This is a consequence of the law of refraction, which says the sine of the angle (I)
from the normal times the refractive index in one material (n i) must equal the sine of the
angle (R) from the normal in the other material times its refractive index (n r): (n i sin I � n r
sin R). Plug in numbers, and you find that light trying to leave the high-index material at
large angles from the normal (I.e., small angles from the surface) would have to emerge
at an angle with sine greater than one. That’s impossible, so the light doesn’t get out. For
a more thorough explanation, see Chapter 2 in Jeff Hecht, Understanding Fiber Optics
3rd ed. (Prentice Hall, Upper Saddle River, N.J., 1999).
B. For a more complete explanation of how the high refractive index of diamond affects
its optical properties, see David Falk, Dieter Brill, and David Stork, Seeing the Light: Optics
in Nature, Photography, Color Vision, and Holography, Harper & Row, New York, 1985,
pp. 63–64.
C. For more on the rainbow and other atmospheric phenomena, see Robert Greenler,
Rainbows, Halos, and Glories (Cambridge University Press, Cambridge, UK, 1980).