Physics for Geologists, Second edition

Optics 45
know whether the light was at B or B1. The principle of reciprocity requires
that light travelling in the reverse directions traverses the same paths. (Do
not forget that light is going out from the point in all directions, but we only
see that which arrives first.)
In Figure 4.3, the light travels from a plane source AA1. When the ray from
A reaches the interface at B, the remainder of the plane wave front BC still
has some distance to travel in air while the ray at B continues in the other
medium. The frequency of the plane wave remains the same, but its speed
changes, so its wavelength also changes. In the time taken for the incident
ray to travel from B' to C', the refracted ray travels a shorter distance (in
this case) from B to C, and the direction of the wave front is altered. The
refracted wave is parallel to CC1.
When the incident light is in the medium with larger refractive index,
smaller speed ci < c, (Figure 4.2(b)), the angle of refraction is larger than
the angle of incidence. As the angle of incidence increases, so the angle of
refraction increases until the refracted ray is in the plane of contact between
the two media and the angle of refraction is 90". This angle of incidence is
called the critical angle, i,, and at any angle of incidence greater than i, the
ray is totally reflected. You can see this when diving. Looking upwards, you
can see things above the surface; but there is an angle i, from the vertical
greater than which the surface appears as a mirror - which indeed it is. Snell's
law tells us that i, = sin-' ci/c, where ci is the speed of light in the denser
medium and c, that in air. This is the inverse of the relationship that gives
the refractive index, so i, = sin-' (lln). For water with a refractive index
of 1.333, the critical angle is about 48.6". For very precise work we would
have to take into account that the speed of light, c, is not quite the same in
air as in a vacuum (the refractive index of air is 1.0002).
Snell's Law applies to the reflection and refraction of sound and seismic
waves as well (see page 107).
Copyright 2002 by Richard E. Chapman
Figure 4.3 Huygen's geometric construction of the refraction path, in section.
When the wave-front AA' reaches BB', it begins to be refracted. The
velocity in the lower medium is less than that in the above, so the
wave only travels the distance BC in the time it takes the wave at B'
to reach C'.