Physics for Geologists, Second edition

Reflection and refraction
Optics 43
When we look in a mirror, we see a reflection of ourselves. We can go further
and measure the angles of reflection by setting a mirror vertically on a piece
of paper on a table and measuring the positions and apparent positions
of pins (Figure 4.1). This is called geometrical optics. Energy radiates from
a source - in this case, the pin - and the lines along which the energy radiates
in different directions are called rays. The rays are perpendicular to the wave-
front of the radiating energy. When they strike a surface, the atoms at that
surface also emit radiation of the same frequency. The basic law of reflection,
which can easily be established by the experiment illustrated in Figure 4.1,
is that the angle of incidence is equal to the angle of reflection. The angle
of incidence is in the plane of incidence, which is normal to the reflecting
surface.
When we look at people standing in a swimming pool, their submerged
parts are distorted. If we dip the end of a straight stick in water at an angle,
it appears to bend upwards at the surface of the water. This is refraction.
Looking along the stick, the apparent angle increases from zero when the
stick is held vertically, to very large as we rotate the stick from the vertical
before we have to abandon the experiment (Figure 4.2(a)). Thus both the
reflected and the refracted rays change direction at an interface, but the fre-
quency remains the same. Viewing the sun rising and setting from near sea
level, its upper limb touches the visible horizon when it is actually about 34'
below the horizon because the rays have been bent by refraction on their
passage through the Earth's atmosphere. The speed of light is greater in
the rarefied air at higher altitudes. Mirages are similarly caused by refrac-
tion, the hot air close to the ground being less dense than the cooler air
higher up.
Copyright 2002 by Richard E. Chapman
Figure 4.1 The angle of reflection, R, is equal to the angle of incidence, i. The
mirror is vertical, perpendicular to the page. The angle of incidence
is in the plane of incidence, which is normal to the mirror, parallel
to the page.