2. Visible light, also known as white light, consists
of a collection of component colors.
These colors are often observed as light passes
through a triangular prism.
Upon passage through the prism, the white light
is separated into its component colors - red,
orange, yellow, green, blue and violet.
The separation of visible light into its different
colors is known as dispersion.
It was mentioned in the Light and Color unit that
each color is characteristic of a distinct wave
frequency; and different frequencies of light
waves will bend varying amounts upon passage
through a prism.
3. Optical density
Different materials are distinguished
from each other by their different optical
densities.
The optical density is simply a measure
of the tendency of a material to slow
down light as it travels through it.
A light wave traveling through a
transparent material interacts with the
atoms of that material.
When a light wave impinges upon an
atom of the material, it is absorbed by
that atom.
4. The absorbed energy causes the
electrons in the atom to vibrate.
If the frequency of the light wave does
not match the resonance frequency of
the vibrating electrons, then the light will
be reemitted by the atom at the same
frequency at which it impinged upon it.
The light wave then travels through the
interatomic vacuum towards the next
atom of the material. Once it impinges
upon the next atom, the process of
absorption and re-emission is repeated.
5.
6. The optical density of a material is the result of
the tendency of the atoms of a material to
maintain the absorbed energy of the light wave in
the form of vibrating electrons before reemitting it
as a new electromagnetic disturbance.
Thus, while a light wave travels through a
vacuum at a speed of c (3.00 x 108 m/s), it
travels through a transparent material at speeds
less than c.
The index of refraction value (n) provides a
quantitative expression of the optical density of a
given medium. Materials with higher index of
refraction values have a tendency to hold
onto the absorbed light energy for greater
lengths of time before reemitting it to the
interatomic void.
7. The more closely that the frequency of
the light wave matches the resonant
frequency of the electrons of the atoms of
a material, the greater the optical density
and the greater the index of refraction.
A light wave would be slowed down to a
greater extent when passing through
such a material.
The index of refraction values are
dependent upon the frequency of light.
For visible light, the n value does not
show a large variation with frequency, but
nonetheless it shows a variation.
8. For instance for some types of glass,
the n value for frequencies of violet
light is 1.53; and the n value for
frequencies of red light is 1.51.
The absorption and re-emission
process causes the higher frequency
(lower wavelength) violet light to travel
slower through crown glass than the
lower frequency (higher wavelength)
red light.
9. It is this difference in n value for the varying
frequencies (and wavelengths) that causes
the dispersion of light by a triangular prism.
Violet light, being slowed down to a greater
extent by the absorption and re-emission
process, refracts more than red light.
Upon entry of white light at the first boundary
of a triangular prism, there will be a slight
separation of the white light into the
component colors of the spectrum.
Upon exiting the triangular prism at the
second boundary, the separation becomes
even greater and ROYGBIV is observed in its
splendor.
10. Angle of Deviation
In optics, the net angular deflection
experienced by a Light Ray after one
or more refractions or reflections.
The total deviation ε of a light ray can
be computed, given the incidence
angle α.
11. The same calculation allows for determination of the
emergence angle δ.
The angle of deviation is the angle between the
original incident ray and the emergent ray.
Since the larger angle of deviation corresponds to a
larger refractive index, violet light would emerge with
the largest angle of deviation and red light would
emerge with the smallest angle.
Hence, the light emerging from the prism would
disperse into a spectrum of rainbow colors wherein
each color corresponds to a different angle of
deviation.
The difference between the angles of deviation of any
two rays is called the angle of dispersion.
12. Rainbow Formation
One of nature's most splendid masterpieces is the
rainbow.
A rainbow is an excellent demonstration of
the dispersion of light and one more piece of evidence
that visible light is composed of a spectrum of
wavelengths, each associated with a distinct color.
To view a rainbow, your back must be to the sun as you
look at an approximately 40 degree angle above the
ground into a region of the atmosphere with suspended
droplets of water or even a light mist.
Each individual droplet of water acts as a tiny prism that
both disperses the light and reflects it back to your eye.
As you sight into the sky, wavelengths of light
associated with a specific color arrive at your eye from
the collection of droplets.
The net effect of the vast array of droplets is that a
circular arc of ROYGBIV is seen across the sky.
13. The Path of Light Through a
Droplet
A collection of suspended water droplets in
the atmosphere serves as a refractor of light.
The water represents a medium with a
different optical density than the surrounding
air.
Light waves refract when they cross over the
boundary from one medium to another.
The decrease in speed upon entry of light
into a water droplet causes a bending of the
path of light towards the normal.
And upon exiting the droplet, light speeds up
and bends away from the normal. The
droplet causes a deviation in the path of light
as it enters and exits the drop.
14. There are countless paths by which light rays
from the sun can pass through a drop.
Each path is characterized by this bending
towards and away from the normal.
One path of great significance in the discussion
of rainbows is the path in which light refracts
into the droplet, internally reflects, and then
refracts out of the droplet.
The diagram at the right depicts such a path.
15. A light ray from the sun enters the droplet
with a slight downward trajectory.
Upon refracting twice and reflecting once, the
light ray is dispersed and bent downward
towards an observer on earth's surface.
Other entry locations into the droplet may
result in similar paths or even in light
continuing through the droplet and out the
opposite side without significant internal
reflection.
But for the entry location shown in the
diagram at the right, there is an optimal
concentration of light exiting the airborne
droplet at an angle towards the ground.
16. As in the case of the refraction of light
through prisms with nonparallel sides,
the refraction of light at two boundaries
of the droplet results in the dispersion of
light into a spectrum of colors.
The shorter wavelength blue and violet
light refract a slightly greater amount
than the longer wavelength red light.
Since the boundaries are not parallel to
each other, the double refraction results
in a distinct separation of the sunlight
into its component colors.
17. The angle of deviation between the incoming light
rays from the sun and the refracted rays directed to
the observer's eyes is approximately 42 degrees
for the red light.
Because of the tendency of shorter wavelength
blue light to refract more than red light, its angle of
deviation from the original sun rays is
approximately 40 degrees.
As shown in the diagram, the red light refracts out
of the droplet at a steeper angle toward an
observer on the ground.
18. There are a multitude of paths by which the
original ray can pass through a droplet and
subsequently angle towards the ground.
Some of the paths are dependent upon which
part of the droplet the incident rays contact.
Other paths are dependent upon the location of
the sun in the sky and the subsequent
trajectory of the incoming rays towards the
droplet.
Yet the greatest concentration of outgoing rays
is found at these 40-42 degree angles of
deviation.
At these angles, the dispersed light is bright
enough to result in a rainbow display in the sky.
19. The Formation of the Rainbow
A rainbow is most often viewed as a circular arc in the
sky. An observer on the ground observes a half-circle of
color with red being the color perceived on the outside
or top of the bow.
Those who are fortunate enough to have seen a
rainbow from an airplane in the sky may know that a
rainbow can actually be a complete circle.
Observers on the ground only view the top half of the
circle since the bottom half of the circular arc is
prevented by the presence of the ground (and the
rather obvious fact that suspended water droplets aren't
present below ground).
Yet observers in an airborne plane can often look both
upward and downward to view the complete circular
bow.
20. The circle (or half-circle) results because there are a
collection of suspended droplets in the atmosphere that
are capable concentrating the dispersed light at angles
of deviation of 40-42 degrees relative to the original
path of light from the sun.
These droplets actually form a circular arc, with each
droplet within the arc dispersing light and reflecting it
back towards the observer.
Every droplet within the arc is refracting and dispersing
the entire visible light spectrum (ROYGBIV).
As described above, the red light is refracted out of a
droplet at steeper angles towards the ground than the
blue light.
Thus, when an observer sights at a steeper angle with
respect to the ground, droplets of water within this line
of sight are refracting the red light to the observer's eye.
21. The blue light from these same droplets is
directed at a less steep angle and is directed
along a trajectory that passes over the observer's
head.
Thus, it is the red light that is seen when looking
at the steeper angles relative to the ground.
Similarly, when sighting at less steep angles,
droplets of water within this line of sight are
directing blue light to the observer's eye while the
red light is directed downwards at a more steep
angle towards the observer's feet.
This discussion explains why it is the red light
that is observed at the top and on the outer
perimeter of a rainbow and the blue light that is
observed on the bottom and the inner perimeter
of the rainbow.
22. Rainbows are not limited to the dispersion of
light by raindrops.
The splashing of water at the base of a
waterfall caused a mist of water in the air that
often results in the formation of rainbows.
A backyard water sprinkler is another common
source of a rainbow. Bright sunlight,
suspended droplets of water and the proper
angle of sighting are the three necessary
components for viewing one of nature's most
splendid masterpieces.
23. Mirages
Most of our discussion of refraction in this unit has
pertained to the refraction of light at a distinct
boundary.
As light is transmitted across the boundary from one
material to another, there is a change in speed,
which causes a change in direction of the light wave.
The boundaries that we have been focusing on have
been distinct interfaces between two recognizably
different materials.
The boundary between the glass of a fish tank and
the surrounding air or the boundary between the
water in a pool and the surrounding air are examples
of distinct interfaces between two recognizably
different materials.
24. It has been mentioned in our discussion that the
refraction or bending of light occurs at the
boundary between two materials; and once a
light wave has crossed the boundary it travels in
a straight line.
The discussion has presumed that the medium
is a uniform medium.
A uniform medium is a medium whose optical
density is everywhere the same within the
medium.
A uniform medium is the same everywhere from
its top boundary to its bottom boundary and
from its left boundary to its right boundary.
But not every medium is a uniform medium, and
the fact that air can sometimes form a non-
uniform medium leads to an interesting
refraction phenomenon - the formation of
25. A mirage is an optical phenomenon that creates
the illusion of water and results from the refraction
of light through a non-uniform medium.
Mirages are most commonly observed on sunny
days when driving down a roadway.
As you drive down the roadway, there appears to
be a puddle of water on the road several yards
(maybe one-hundred yards) in front of the car. Of
course, when you arrive at the perceived location
of the puddle, you recognize that the puddle is not
there. Instead, the puddle of water appears to be
another one-hundred yards in front of you.
You could carefully match the perceived location of
the water to a roadside object; but when you arrive
at that object, the puddle of water is still not on the
roadway. The appearance of the water is simply an
illusion.
26. Mirages occur on sunny days. The role
of the sun is to heat the roadway to high
temperatures.
This heated roadway in turn heats the
surrounding air, keeping the air just
above the roadway at higher
temperatures than that day's average air
temperature.
Hot air tends to be less optically dense
than cooler air. As such, a non-uniform
medium has been created by the heating
of the roadway and the air just above it.
27. While light will travel in a straight line through a
uniform medium, it will refract when traveling
through a non-uniform medium.
If a driver looks down at the roadway at a very
low angle (that is, at a position nearly one
hundred yards away), light from objects above
the roadway will follow a curved path to the
driver's eye as shown in the diagram below.
28. Light that is traveling downward into this less
optically dense air begins to speed up.
Though there isn't a distinct boundary between
two media, there is a change in speed of a light
wave. As expected, a change in speed is
accompanied by a change in direction. If there
were a distinct boundary between two media, then
there would be a bending of this light ray away
from the normal.
For this light ray to bend away from
the normal (towards the boundary), the ray would
begin to bend more parallel to the roadway and
then bend upwards towards the cooler air. As
such, a person in a car sighting downward at the
roadway will see an object located above the
roadway.
29. Of course, this is not a usual event.
When was the last time that you looked downward
at a surface and saw an object above the surface?
While not a usual event, it does happen.
For instance, suppose you place a mirror on the
floor and look downward at the floor; you will see
objects located above the floor due to the reflection
of light by the mirror. Even a glass window placed
on the floor will reflect light from objects above the
floor.
If you look downward at the glass window at a low
enough angle, then you will see objects located
above the floor. Or suppose that you are standing
on the shore of a calm pond and look downward at
the water; you might see objects above the pond
due to the reflection of light by the water.
30. So when you experience this sunny day
phenomenon, your mind must quickly make
sense of how you can look downward at the
roadway and see an object located above the
road. In the process of making sense of this
event, your mind draws upon past experiences.
Searching the database of stored experiences,
your mind is interested in an explanation of why
the eye can sight downward at a surface and see
an object that is located above the surface.
In the process of searching, it comes up with
three possible explanations based upon past
experiences. Your mind subtly ponders these
three options.
31. There is a mirror on the road. Someone
must have for some reason placed a
mirror on the road.
The mirror is reflecting light and that is
why I see an image of the oncoming
truck when I look downward at the road.
There is a glass window on the road. My
gosh, do you believe it! Someone has
left a glass window on the road.
The glass window is reflecting light and
that is why I see an image of the
oncoming truck when I look downward at
the road.
32. There is water on the road. It must have rained
last night and there is a puddle of water left on
the road.
The water is reflecting light and that is why I
see an image of the oncoming truck when I
look downward at the road.
Of the three possible explanations of the
image of the truck, only one makes a lot of
sense to the mind - there is water on the road.
After all, while both glass windows and mirrors
can reflect light, nowhere in your mind's
database of past experiences is there an
account of a mirror or glass window being
seen on a roadway.
33. Yet there are plenty of times that a water
puddle has been observed to be present on a
roadway.
Smart person that you are, you then conclude
that there is a puddle of water on the road that
is causing you to see objects located above
the road when you sight downward at the
road. The illusion is complete.
34. Reference
http://www.askiitians.com/iit-jee-ray-optics/prism/
http://violet.pha.jhu.edu/~wpb/spectroscopy/measure.ht
ml
http://www.timbercon.com/Angle-of-Deviation.html
http://www.slideshare.net/Sciencetutors/light-dispersion-
spectrumrefraction-reflection-presentation
http://www.physicsclassroom.com/class/refrn/u14l4a.cf
m
http://www.vikdhillon.staff.shef.ac.uk/teaching/phy217/in
struments/phy217_inst_dispersion.html
http://www.blurtit.com/q7949233.html
http://www.physicsclassroom.com/class/refrn/U14l4c.cf
m
http://www.physicsclassroom.com/class/refrn/U14l4b.cf
m
http://en.wikipedia.org/wiki/Dispersion_%28optics%29
