LIGHT

1. Light travels very fast but its speed is not infinite. Early attempts to measure the speed
using earth based experiments failed. Then in 1675 the astronomer Roemer studied timing
of the eclipse of one of Jupiter's moon called Io. In the diagram below Io is observed with
Earth at A and then at C. The eclipse is 16.6 minutes late, which is the time taken for light
to travel AC. Roemer estimated that 3 108 metres/sec, a value that is remarkably
close to the best modern measurement, 299792458.6 metres/sec.
c
c
= ×
=
2. Light is electromagnetic waves. Different frequencies correspond to different colours.
Equivalently, different wavelength correspond to different colours. Recall that the product
c.
ν
λ
ν ×λ =
-9
In the diagram below you see that visible light is only one small part of the total
electromagnetic spectrum. Here nm means nanometres or 10 metres.
3. If light contained all frequencies with equal strength, it would appear as white to us.
course, most things around us appear coloured. That is because they radiate more strongly
in one range of frequency than in others. If there is more intensity in the yellow range
than the green range, we will see mostly yellow. The sky appears blue to us on a clear
day because tiny dust particles high above in the atmosphere reflect a lot of the blue light
coming from the sun. In the figure below you can see the hump at smaller wavelengths.
Compare this with the spectrum of light emitted from a tungsten bulb. You can see that
this is smoother and yellow dominates.
4. What path does light travel upon? If there is no obstruction, it obviously likes to travel on
straight line which is the shortest path between any two points, say A and B. Fermat's
Principle states that in all situations, light will always take that path for which it takes the
least time. As an example, let us apply Fermat's Principle to the case of light reflected from
a mirror, as below.
The total distance travelled by the ray is 2 2 2 ( )2 . The time taken
is / . To find the smallest time, we must differentiate and then set the derivative
to zero, 0
L a x b d x
t L c
dt
dx
= + + + −
=
=
( ) ( ) ( ) ( )( )( )
( )
2 2 1/ 2 2 2 1/ 2
2 2 2 2
1 1
1
1 2 1 2 1
2 2
From here we immediately see that From the
above diagram, sin sin . Of course, it is n
dL
c dx
a x x b d x d x
c c
x d x
a x b d x
θ θ
−
=
= + + ⎡⎣ + − ⎤⎦ − −
−
=
+ + −
= ′ o surprise that the angle of reflection
equals the angle of incidence. You knew this from before, and this seems like a very
complicated derivation of a simple fact. But it is still nice to see that there is a deeper
principle behind it.
Normal Daylight
400nm 500nm 600nm 700nm
Intensity
Tungsten Bulb
400nm 500nm 600nm 700nm
Intensity
1 θ
1 θ
1 θ
′
1 θ
′
d
x d−x
a b
A
B
1 θ
1 θ
d
x d−x
a
b
2 θ
2 θ
1 L
2 L
1 n
2 n
1 v
2 v
A
C
5. The speed of light in vacuum is a fixed constant of nature which we usually call , but in
a medium light can travel slower or faster than . We define the "refractive index" of that
medium
c
c
as: Refractive index Speed of light in vacuum (or ). Usually the values
Speed of light in material v
of are bigger than one (e.g. for glass it is around 1.5) but in some special media, its va
n c
n
= =
lue
can be less than one. The value of also depends on the wavelength (or frequency) of light.
This is called dispersion, and it means that different colours travel at different speeds insid
n
e
a medium. This is why, as in the diagram below, white light gets separated into different
colours. The fact that in a glass prism blue light travels faster than red light is responsible
for the many colours we see here.
6. We can apply Fermat's Principle to find the path
followed by a ray of light when it goes from one
medium to another. Part of the light is reflected,
and part is "refracted", i.e. it be
( )
1 2 11 2 2
1 2
2 2 2 2
1 1 2 2 1 2
nds away or
towards the normal. The total time is,
,
v v v
Fermat's Principle says that the time must be
t L L n c t nL nL L
c c
L nL nL n a x n b d x
t
+
= + = ⇒ = =
= + = + + + −
( ) ( ) ( ) ( )( )( )
( )
1 2 2 1/ 2 2 2 2 1/ 2
1 2 2 2 2 2 1 1 2 2
minimized: 0 1 2 2 1
2 2
And so we get "Snell's Law", or sin sin . This
required a little bit of mathematics, but you c
dt dL n a x x n b d x d x
dx c dx c c
n x n d x n n
a x b d x
θ θ
− = = = + + ⎡⎣ + − ⎤⎦ − −
−
= =
+ + −
an see how powerful Fermat's Principle is!
7. Light coming from air into water bends toward the normal. Conversely, light from a
source in the water will bend away from the normal. What if you keep increasing the
angle with respect to the normal so that the light bends and begins to just follow the
surface? This phenomenon is called total internal reflection and is called the criti c
θ cal
1 n
2 n
c θ
0 12
1 2
1
angle. It obeys: sin sin90 from which sin . c c
n n n
n
θ = θ = −
8. Fibre optic cables, which are now common everywhere, make use of the total internal
reflection principle to carry light. Here is what a fibre optic cable looks like from inside:
Even if the cable is bent, the light will continue to travel along it. The glass inside the
cable must have exceedingly good consistency - if it thicker or thinner in any part, the
refractive index will become non-uniform and a lot of light will get lost. Optical fibres
now carry thousands of telephone calls in a cable whose diameter is only a little bigger
than a human hair!