From: Ronald Wong (ronwong@inreach.com)
Date: Thu Mar 07 2002 - 14:59:30 PST
Message-Id: <l03102800b8ad7f6defc9@[209.209.19.211]> Date: Thu, 7 Mar 2002 14:59:30 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: re rainbows/prisms and why light bends
Regan:
The answer to your question regarding the bending of light as it passes
from air into a prism has two parts.
A. Speed
The first part has to do with the fact that the speed of light has
undergone a change as it moved from one medium to another (air into glass
in your case).
Paul's explanation as to why the beam of light travels slower in a
transparent medium than in space is as good as it gets.
If you want an analogy for your kids as to why light travels faster in a
vacuum than in a transparent medium, have them consider the following:
There is a large, empty warehouse and a student is trying to get from one
end of the warehouse to the other by walking briskly across the floor of
the warehouse.
If there is no one around, he can get to the other side in very little time.
If there are people standing around in the warehouse that he is dying to
interact with then, although he may be moving just as briskly as before as
he goes from one person to another, he is going to take longer to get to
the other side due to his interaction with the individuals he encounters
along the way.
The greater the amount of interaction with each of the individuals, the
longer it takes him to get to the other side.
Light is like this. In a vacuum, it interacts with nothing and gets from
one point in space to another in a very short time due to it's incredible
speed of 299 792 458 m/s. In a transparent substance, it interacts with the
outer electrons of the substance's atoms as per Paul's explanation. As a
result, it takes longer to travel the same distance in the transparent
medium than it would in a vacuum.
This is what we mean when we say that light "travels slower" in a
transparent medium. It's STILL traveling at 299 792 458 m/s as it moves
from one atom to the next but, as a result of the interactions with the
atoms, it takes longer to get from one point to another in space than if
the atoms hadn't been present.
In general, the further from the UV frequencies, the less the interaction.
So violet light, whose frequency is closer to the UV and who will therefore
interact with the atoms to a greater degree, travels slower through the
transparent medium than red whose interaction is less due to it's lower
frequency.
B. The angle of incidence
The difference in speed is, by itself, NOT enough to explain the bending.
If the light beam crosses from one medium into another where it's speed is
different and does so "head on" (direction of travel is perpendicular to
the boundary between the two mediums) it WON'T bend.
To undergo bending, it must cross the boundary at an oblique.
This is true for all wave phenomena of which light is only one example.
This change in direction that a wave experiences as it passes obliquely
from one medium into another while undergoing a change in speed is called
refraction.
It is a property of sound waves, water waves, waves produced by
earthquakes, electromagnetic waves, etc.
The need for obliqueness - in addition to a change in speed - has to do
with the fact that crossing a boundary at an oblique produces a condition
where one part of a given wave front will experience a change in speed
before another.
The classic analogy to explain why this should lead to refraction is the
column of marching soldiers/marching-band that finds itself marching from
solid ground into a marsh at an oblique angle.
Along a given row, the soldiers that enter the marsh first slow down and
take smaller steps (in the case of light, the wavelength decreases) while
keeping the cadence of the march (in the case of light, the frequency
remains unchanged). If you were to draw the consequences of this action on
the board, you would see that the line of march (the direction the marchers
are moving) is rotated towards a line drawn perpendicular to the boundary
between the marsh and the solid ground (when the wave slows down while
passing obliquely from one medium into another it "bends towards the
normal").
The muddier the marsh, the smaller the steps and the greater the bending.
Thus, violet light with it's greater interaction experiences the greater
foreshortening of its wavelength and the greater bending (remember,
velocity = frequency times wavelength. Since the frequency remains
unchanged when undergoing refraction, the reduction in velocity leads to a
corresponding reduction in wavelength).
Here's an URL that offers an activity that your students can do that will
demonstrate the above comments (Courtesy of Glenbrook South High School in
Glenview, Illinois):
http://www.glenbrook.k12.il.us/gbssci/phys/Class/refrn/u14l1c.html
You might want to look at what else they have to offer in their tutorial
for high school physics.
Cheers.
ron
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