Optics

More familiar types of waves are sound, or waves on a surface of water. In both cases, there is a
perturbation with a periodic spatial pattern which propagates, or travels in space. In the case
of sound waves in air for example, the perturbed quantity is the pressure, which oscillates about
the mean atmospheric pressure. In the case of waves on a water surface, the perturbed quantity
is simply the height of the surface, which oscillates about its stationary level. Figure 1.1 shows
an example of a wave, captured at a certain instant in time. It is simpler to visualize a wave by
drawing the “wave fronts”, which are usually taken to be the crests of the wave. In the case of
Figure 1.1 the wave fronts are circular, as shown below the wave plot.
1.1.2 Evidence for wave properties of light
There are certain things that only waves can do, for example interfere. Ripples in a pond caused
by two pebbles dropped at the same time exhibit this nicely: Where two crests overlap, the waves
reinforce each other, but where a crest and a trough coincide, the two waves actually cancel. This
is illustrated in Figure 1.2. If light is a wave, two sources emitting waves in a synchronized fashion1
should produce a pattern of alternating bright and dark bands on a screen. Thomas Young tried
the experiment in the early 1800’s, and found the expected pattern.
The wave model of light has one serious drawback, though: Unlike other wave phenomena such as
sound, or surface waves, it wasn’t clear what the medium was that supported light waves. Giving
it a name – the “luminiferous aether” – didn’t help. James Clerk Maxwell’s (1831 - 1879) theory of
electromagnetism, however, showed that light was a wave in combined electric and magnetic fields,
which, being force fields, didn’t need a material medium.
1When two sources of waves oscillate in step with each other, they are said to be coherent. We will return to
this when we study interference phenomena in greater detail.
1.2. FEATURES OF A WAVE 3
1.1.3 Evidence for light as a stream of particles
One of the earliest proponents of the idea that light was a stream of particles was Isaac Newton
himself. Although Young’s findings and others seemed to disprove that theory entirely, surprisingly
other experimental evidence appeared at the turn of the 20th. century which could only be explained
by the particle model of light! The photoelectric effect, where light striking a metal dislodges
electrons from the metal atoms which can then flow as a current earned Einstein the Nobel prize
for his explanation in terms of photons.
We are forced to accept that both interpretations of the phenomenon of light are true, although
they appear to be contradictory. One interpretation or the other will serve better in a particular
context. For our purposes, in understanding how optical instruments work, the wave theory of light
is entirely adequate.
1.2 Features of a wave
We’ll consider the simple case of a sine wave in 1 dimension, as shown in Figure 1.3. The distance
between successive wave fronts is the wavelength.
As the wave propagates, let us assume in the positive x direction, any point on the wave pattern
is displaced by dx in a time dt (see Figure 1.4). We can speak of the propagation speed of the
wave
v = dx
dt
(1.1)
As the wave propagates, so do the wavefronts. A stationary observer in the path of the wave
would see the perturbation oscillate in time, periodically in “cycles”. The duration of each cycle
is the period of the wave, and the number of cycles measured by the observer each second is the
frequency2. There is a simple relation between the wavelength , frequency f, and propagation
speed v of a wave:
v = f (1.2)
Electromagnetic waves in vacuum always propagate with speed c = 3.0 × 108 m/s. In principle,
electromagnetic waves may have any wavelength, from zero to arbitrarily long. Only a very narrow
range of wavelengths, approximately 400 - 700 nm, are visible to the human eye. We perceive
wavelength as colour; the longest visible wavelengths are red, and the shortest are violet. Longer