Theories of light
In the seventeenth century two rival theories of the nature of light were proposed, the
wave theory and the corpuscular theory .
The Dutch astronomer Huygens (1629-1695) proposed a wave theory of light. He
believed that light was a longitudinal wave, and that this wave was propagated
through a material called the 'aether'. Since light can pass through a vacuum and
travels very fast Huygens had to propose some rather strange properties for the aether:
for example; it must fill all space and be weightless and invisible. For this reason
scientists were sceptical of his theory.
In 1690 Newton proposed the corpuscular theory of light. He believed that light was
shot out from a source in small particles, and this view was accepted for over a
hundred years.
The quantum theory put forward by Max Planck in 1900 combined the wave theory
and the particle theory, and showed that light can sometimes behave like a particle
and sometimes like a wave. You can find a much fuller consideration of this in the
section on the quantum theory.
Wave theory of Huygens
As we have seen, Huygens considered that light was propagated in longitudinal
waves through a material called the aether. We will now look at his ideas more
closely.
Huygens published his theory in 1690, having compared the behavior of light not with
that of water waves but with that of sound. Sound cannot travel through a vacuum but
light does, and so Huygens proposed that the aether must fill all space, be transparent
and of zero inertia. Clearly a very strange material .
Even at the beginning of the twentieth century, however, scientists were convinced of
the existence of the aether. One book states 'whatever we consider the aether to be
'there can be no doubt of its existence.
We now consider how Huygens thought the waves moved from place to place
Consider a wavefront initially at position W, and assume that every point on that
wavefront acts as a source of secondary wavelets. (Figure 1 shows some of these
secondary sources). The new wavefront W1 is formed by the envelope of these
secondary wavelets since they will all have moved forward the same distance in a
time t (Figure 1) .
There are however at least two problems with this idea and these led Newton and
others to reject it :
a) the secondary waves are propagated in the forward direction only, and(
b) they are assumed to destroy each other except where they form the new wavefront
Newton wrote: 'If light consists of undulations in an elastic medium it should diverge
in every direction from each new center of disturbance, and so, like sound, bend round
all obstacles and obliterate all shadow.' Newton did not know that in fact light does do
this, but the effects are exceedingly small due to the very short wavelength of light
Huygens' theory also failed to explain the rectilinear propagation of light
The reflection of a plane wavefront by a plane mirror is shown in Figure 2. Notice the
initial position of the wavefront (AB), the secondary wavelets and the final position of
the wavefront (CD). Notice that he shape of the wavefront is not affected by reflection
at a plane surface.
The lines below the mirror show the position that the wavefront would have reached if
the mirror had not been there.
We will now show how Huygens' wave theory can be used to explain reflection and
refraction and the laws governing them.
a) Reflection
Consider a parallel beam of monochromatic light incident on a plane surface, as
shown in Figure 3. The wave fronts will be plane both before and after reflection,
since a plane surface does not alter the shape of waves falling on it.
Consider a point where the wavefront AC has just touched the mirror at edge A.
While the light travels from A to D, that from C travels to B. The new envelope for
the wavefront AC will be BD after reflection.
Therefore: AD = CB, Angle ACB = angle ADB = 90o, AB is common
Therefore ΔACB and ΔBDA are similar and so angle CAB = angle BAD.
Therefore i = r and the law of reflection is proved.
b) Refraction
consider a plane monochromatic wave hitting the surface of a transparent material of
refractive index n. The velocity of light in the material is cm and that in air ca. Now in
,Figure 4
CB = AB sin i
AD = AB sin r
The same argument applies about the new envelope as in the case of reflection
time to travel CB = CB/ca = AB sin i/ca
time to travel AD = AD/cm = AB sin i/cm
But these are equal and therefore
ca/cm = sin i/sin r = anm
This is Snell's law, and it was verified later by Foucault and others
Notice that since the refractive index of a transparent material is greater than 1,
Huygens' theory requires that the velocity of light in air should be greater than that in
the material
Corpuscular theory of Newton
Newton proposed that light is shot out from a source as a stream of particles. He
argued that light could not be a wave because although we can hear sound from
behind an obstacle we cannot see light - that is, light shows no diffraction. He stated
that particles of different colours should be of different sizes, the red particles being
larger than the blue.
Since these particles are shot out all the time, according to Newton's theory, the mass
of the source of light must get less
We can use Newton's theory to deduce the laws of reflection and refraction
a) Reflection
Consider a particle of light in collision with a mirror. The collision is supposed to be
perfectly elastic, and so tile component of velocity perpendicular to the mirror is
.reversed while that parallel to the mirror remains unaltered
Component of velocity before collision parallel to the mirror = ca sin i
Component of velocity after collision parallel to the mirror = ca sin r
Therefore:
ca sin i = ca sin r
and so the law of reflection is proved
(b) Refraction
Newton assumed that there is an attraction between the molecules of a solid and the
particles of light, and that this attraction acts only perpendicularly to the surface and
only at very short distances from the surface. (He explained total internal reflection by
saying that the perpendicular component of velocity was too small to overcome the
molecular attraction.) This has the effect of increasing the velocity of the light in the
material.
Let the velocity of light in air be ca and the velocity of light in the material in Figure 6
be cm.
The velocity parallel to the material is unaltered and therefore:
casin i = cmsin r
Therefore:
cm/ca = sini/ sinr = anm
This ratio is the refractive index, but because n > 1 the velocity of light in the material
must be greater than that in air. Newton accepted this result and other scientists
preferred it to that of Huygens, mainly because of Newton's eminence.
A problem of the corpuscular theory was that temperature has no effect on the
velocity of light, although on the basis of this theory we would expect the particles to
be shot out at greater velocities as the temperature rises.
Classical and modern theories of light
It is interesting to compare the two classical theories of light and see which
phenomena can be explained by each theory. The following table does this Wave
Wave theory
Reflection
Refraction
Diffraction
Interference
Corpuscular theory
Reflection
Photoelectric effect
Notice that neither theory can account for polarization, since for polarization to occur
the waves must be transverse in nature.
Modem theories:
Twentieth-century ideas have led us to believe that light is
a) a transverse electromagnetic wave with a small wavelength, and
b) emitted in quanta or packets of radiation of about 10-8 s duration with abrupt phase
changes between successive pulses.