Multiple Light Source and Shadows
I noticed a phenomenon the other day and I wonder
if someone could explain it. I will do my best to outline it. A)
I have a lamp over my desk that holds 4-40W incandescent bulbs
lined up in a row. I will label the bulbs # 1;2;3;4 from left to
right. B) While sitting at my desk holding a pen I noticed there
were four shadows of the pen on my desk's surface; I will label
the pen shadows # 1;2;3;4 from left to right C) suddenly bulb 3
burned out, but pen shadow 2 disappeared. D) I would have
expected shadow 3 to disappear. What is going on here? Also: If
you have 4 light bulbs shining on an object the object will give
off 4 shadows. Why? Wouldn't there just be one shadow from the
light of the 4 bulbs. Doesn't the light combine into one light?
Having 4 shadows implies that the light from each bulb remains separate?
You are absolutely right! The light from each of the four bulbs
travels in straight lines and is unaffected by the light from the
other bulbs. This is true until the light intensity reaches really
incredible levels (which would certainly blind you instantly).
Therefore the bulb furthest to the right makes a shadow of the
pencil furthest to the left. In your notation, bulb 1 makes shadow
4, 2 makes 3, 3 makes 2 and 4 makes 1. A rough sketch drawing
straight lines from the four bulbs through the pencil to the surface
of the desk will allow you to predict and understand exactly what
you see. Enjoy!
Best, Dick Plano, Professor of Physics emeritus, Rutgers University
It is perhaps best to describe the observed phenomena by using what
is known as "ray tracing." Each light bulb has a filament inside
which heats up and produces light. As such, each light bulb acts as
a distinct light source. Filaments can be a few millimeters in
size, but for simplicity, we here consider each to be a small bright
spot, or in the technical jargon, as a point source.
Consider now one of the spots. The light emanating from it goes
almost everywhere, all around. The part that strikes the pen is
blocked but the rest continue until they strike the desk surface and
the surrounding area. This blockage of light by the pen is what
produces the shallow. You can trace out this shadow even without
the light on. To do that, you would draw (imaginary) straight lines
from small bright spot tracing out the outer edges of the pen and
continuing until they strike the desk surface. What you will have is
the shadow of the pen traced out in three dimensions and projected
onto the desk. Ray tracing on paper by drawing a point can
demonstrate the essentials, a circle some distance from it, and a
straight line further out. These are two-dimensional representations
of your light bulb, pen, and desk surface, respectively. You can
draw two and only two straight lines from the point tangent to the
circle. Continue these lines until the strike the desk-surface line
in two points. The area between these two points and the circle is
the shadow region of the circle.
Now, draw three more point sources next too the original one. For
clarity, it is best if the line passing through the point sources is
parallel to the line that represents the desk surface. Tracing out
rays from each point source to the circle indicates that you will
have four shadows. (Please keep in mind that the distances from
source to the circle and the line, and the size of the circle are
important variables.) For example, the four shadows will be
distinct if the line representing the desk surface is drawn close to
the circles.) If you look at your ray tracing, you will note that
the light from the second light source produces the third shadow and so on.
This all is due to the fact that light can be thought of as
particles (photons) emanating from the source and interacting with
the obstacle. The shadow (or the image) can be determined by ray
tracing as described.
If the light source is NOT a point source, things get a little more
complex because you have to consider (trace out) photons originating
from different parts of the source. In this situation the shadows
will be more complex, and interesting.
Ali Khounsary, Ph.D.
Argonne National Laboratory
Light travels through the air in straight lines. An object's shadow
is where the light does not reach because it is blocked by the
object. Thus, if the light comes from the right side of an object
the shadow will be on the object's left side.
Each light bulb is a separate source of light. Light from each bulb
travels in a straight line from the bulb to the pen to the
desktop. Hence, each bulb casts its own shadow.
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Update: June 2012