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Name: Frank
Status: other
Age: N/A
Location: NY
Country: US
Date: N/A


Question:
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?



Replies:
Dear Frank,

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


Frank,

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.

Greg Bradburn



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