| You've all seen the rainbow-like spectrum
created by white light through a prism. The colors spread
out because the shorter wavelengths -- the blues --- are
bent more than the longer wavelengths as they pass or
refract through the prism. |
 |
 |
| But why is light bent when it enters a higher
index material at an angle? Due to the higher index of
refraction, the speed of light is less in glass, say,
than it is in air. The frequency is always the same no
matter what the medium, so it's the wavelength that shortens
in a higher index material. |
| To show you the prism effect, I used a "carbon
arc lamp". This is a device for producing intense
white light by striking a high voltage electric spark
between the tips of two carbon rods. |
 |
 |
Carbon arc lamps pre-date Thomas Edison's first electric
light, and were a motivation for Edison to create something
cleaner and safer to use. |
| Movie theaters used carbon arc projection
lamps up until recently, and the expression "in the
limelight" comes from a similar device using limestone
instead of carbon to produce intense light for lighthouses. |
| If light passes through two slits close
together, each slit will act as an independent source
of light. Because light bends around the corners of the
slits (by diffraction) the spread of light on a screen
far away will be made of a variety of path lengths interfering
with each other. If the path lengths differ by one whole
wavelength, the light from each slit combines to produce
a bright spot. If the path lengths differ by half a wavelength,
you get a dark spot. |
|
The spacing of the bright spots is governed by simple
geometric relations:
d sin θ= ΔL
= mλ and tan θ = y/D
and knowing that θ
is very small, gives y
= mλ D/d where m is an integer and is called
the "order" of interference --- first bright
spot measured from the center is m = 1, third bright
spot is m = 3, etc.
|
 |
|
Note that the spacing between orders (m+1) and (m)
is just y = λD/d,
which is the spacing between any two interference maxima
or minima.
|
 |
| If you can vary the slit separation, you
can easily see that as the slits get farther apart, the
pattern gets "tighter" or the maxima get closer
together. If the slits separation gets less, the pattern
"spreads out" or the maxima get farther apart.
This effect isn't limited to two slits. You can get
the same results if you have a barrier in the path of
a light beam, like a human hair. The light will bend
around the edges of the hair and the light paths from
each side of the hair will interfere with each other.
In this case, the "slit separation, d" is
the width of the hair.
By measuring the interference pattern and deducing
"y", and knowing the wavelength ? and distance
to the screen D, I found that the hair from my head
was 55 microns wide. I also found the hair from my mustache
was 160 microns wide! For most men, this is the case
--- head hair is a lot finer than facial hair. (Facial
hair also tends to be rectangular rather than round!)
In manufacturing, you can use this technique to monitor
the diameter of fine wire that might be used in electronic
devices.
See? Knowing physics really is useful!
|
