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| Lunar Eclipse |
The formation of shadows
Light travels on straight lines
Experiment: The next time you go outside on a clear day,
take 10 or so pencils or equivalent long objects with you.
Over an area of several square meters (yards), stick the pencils
in the ground at an angle so they do not cast shadows.
These pencils then show you the ray directions all over the area.
They will all be parallel to each other.
The pencils will help you imagine all the parallel sunlight striking
the Earth.
Sunlight is parallel, so its shadows remain the same size as the object's
profile.
A desk lamp or a street light also casts shadows because the light
is streaming out in all directions away from the source.
However, since its rays are not parallel, shadows get bigger farther
away from the object.
Experiment: Set up a bare lamp on one side of a room.
Stand near the opposite wall, and observe the size of your shadow.
Walk toward the lamp and watch your shadow grow on the wall.
Umbra and penumbra from an extended source
The evenly dark part of a shadow is called the umbra.
Umbra means 'shade' in Latin.
The fuzzy part between the dark and the light is called the
penumbra.
Pene means 'almost' in Latin.
If one is in the umbra of an object, the light source is completely
obscured.
If one is in the penumbra, the source is only partially obscured,
to a greater or lesser degree as one moves through the penumbra.
The umbra of a shadow is not absolutely black because there is
always scattered light that makes its way into it.
In the case of sunlight, the scattered light is mostly bluish
sky light, so shadows are bluer than normal.
The Impressionist painters were the first to recreate
this blueness.
Experiment: On a sunny winter day with snow on the ground,
observe the color of shadows.
The first of the great Greek natural philosophers Thales of
Miletos (580 BCE) understood that eclipses of the Sun
and the Moon are related to the shadows of the Moon and the Earth.
During an eclipse of the Sun, the shadow of the Moon sweeps accross
the Earth.
We see the Sun blocked by the Moon.
During an eclipse of the Moon, the Moon passes through the
Earth's shadow.
Here is a diagram of what the shadow of a planet in space looks like.
And here is the Earth/Moon system drawn to scale.
At the distance of the Moon, the Earth's umbra is about three times
the diameter of the Moon and 3/4 the diameter of the Earth.
In the title picture at the top of this page, the umbra covers
about 3/4 of the Moon.
The bright portion at the top is penumbral shadow.
The umbra is not perfectly dark because sunlight scattering through
the Earth's atmosphere is able to illuminate the Moon.
An astronaut standing on the Moon during this eclipse would see
the Earth completely blocking the Sun, but would also see the
bright red rim of sunset/sunrise glow all around the Earth.
One can trace the curvature of the umbra and measure the size of the
Earth's shadow directly.
This observation led the Greek astronomer Aristarchos (300 BCE)
to accurately conclude that the Moon is 1/4 the size of the Earth and
30 Earth diameters away.
For more photographs and information on upcoming eclipses, see the
MrEclipse
web pages.
The pinhole camera
A pinhole camera casts an inverted image on the back.
This image will also be slightly blurry, because light coming from
one atom on the object is spread out over the back of the camera
according to the size of the pinhole.
Each disk of light cast onto the back overlaps and blurs with
disks from nearby atoms.
One can reduce the blur by making the pinhole smaller.
However, then the image becomes darker and may not be visible
or recordable on film.
How to make a pinhole viewer
Diffraction
The diffraction of sound waves allows one to hear
the voice of someone in another room.
Since light has wave properties, it, too, diffracts.
If you look at the ocean waves carefully, you will notice that
waves passing several wavelengths to the left of the
end of the jetty continue virtually undisturbed.
Only the waves passing close to the end curve into the "shadow"
of the jetty.
The same is true for light.
Consider again the pinhole camera.
Light does not have to be deflected very much to cause a blurring
of the image.
An approximate formula for the blur width B from the edges
of a pinhole is
B ≈ Dw/d
where D is the distance from the hole to the back of the camera,
w is the wavelenth of the light, and d is the diameter
of the hole.
The simple blur caused the diameter of the hole is about equal to d
itself.
The two blurs are equal when d ≈ √(Dw).
Measuring everything in millimeters and assuming the wavelength of
visible light is about 0.0005 mm, the minumum useful diameter of a
pinhole is about .02√D mm.
If the camera is 300 mm (about 1 foot) long, the minimum hole size
becomes about 1/3 mm.
Here are two good web resources on diffraction:
Summary:
The perception of shadows (how it is that we recognize a shadow
for what it is) is very interesting and will be discussed in a later
module.
Our brains have even learned how to guage depth from the fuzziness
of penumbras.
Sample questions for reflection
How do shadows form?
What determines the "shape" of a shadow?
Why are most shadows fuzzy-edged?
What is the umbra, penumbra of a shadow?
Why are sunlight shadows bluish in color?
What causes an eclipse of the Moon?
How did Aristarchus measure the size and distance of the Moon?
How does a pinhole camera produce an image?
What is diffraction?
What are the two reasons why a pinhole camera makes fuzzy images?
We can use ray tracing to track where light goes after it leaves
a source.
If it scatters off something, we just re-direct our ray and follow
it from there.
Cast shadows occur when some object blocks rays from
reaching a surface.
For a shadow to be clearly visible, much of the light in the space
around the object must be coming from a relatively small or
distant source, so it is all moving in orderly directions.
Sunlight casts clear shadows because the Sun is far away and
small in the sky.
When sunlight gets to Earth, it is all nearly self-parallel.
You may have noticed that shadows are often fuzzy, particularly
when the surface on which the shadow lies is far from the object
casting the shadow.
This fuzziness is because no light source is only a point in space.
All sources have some geometrical size.
Thus, light from one edge of the source is not quite parallel to light
from the other edge.
Vincent van Gogh Orchard in Bloom with Poplars, 1889.
WebMuseum
A pinhole camera is a camera obscura, just like
Alhazen's
dark room with a small window.
The word camera comes from the Greek kamara, a vaulted
chamber.
Rays scatter off objects in all directions.
The pinhole in the front of the camera selects only the rays
traveling in the direction of the pinhole.
These rays pass into the camera and strike the back surface.
The front and side walls shade that point on the back from
rays coming from different points of origin.
My mother-in-law in our spring garden
How to make a pinhole camera
When waves encounter an obstacle with an edge, some of the wave
energy bends around the edge behind the obstacle.
This bending is called diffraction.
Here is a picture of ocean waves moving around a jetty.
A smaller the diameter of the hole gives a greater blur by diffraction.
General principles.
A java applet with adjustable hole and wavelength.
Light travels in straight lines, and is either blocked
or scattered by objects in its path.
Extended sources cast shadows with fuzzy edges.
The fully dark part is called the umbra, and the fuzzy part is called
the penumbra.
Eclipses happen when one astronomical object passes into the
shadow of another object.
Pinholes select rays for projection onto the back of a pinhole camera.
The action whereby waves bend around obstacles is called diffraction.
Diffraction causes blurry images in a pinhole camera if the hole is too
small.
Which one is more important for small holes? Large holes?