Shadows

Light travels in straight lines.

Sunlight creates straight line shadows in the air.

Introduction

A point of light casts a sharp-edged shadow.  The shadow can be traced on paper. The size of the shadow depends on the size of the object, the distance from the light to the object and the distance from the light to the screen.

Material

A bright point of light. The bare bulb of a minimaglight or sunlight reflected off a mirrored sphere.

A sheet of paper on a firm backing.

Pencils for drawing the shadow.

Assembly

Set up the point of light and a white screen. Place an object between the light and the screen.

To Do and Notice

Observe the shadow of the object.

Change the size of the shadow by moving the point of light, the object and the screen.

When you achieve a shadow size and shape you like trace it on the screen.

Going Further

Make the object the profile of the face of a person.

Trace the shadow. Near the edge of the paper facing outward.

Fold the paper in half.

Then cut the shadow tracing out of the paper.

You will have a symmetrcal vase-like shape.

Place the vase on contrasting paper.

The human profile is turned into a vase.

In the image below the shadow was already a symmetrical object.

What's Going On?

Light travels in straight lines.

Light traveling from a point to a screen over the top of an object makes a straight line.

Light traveling from a point to a screen under the bottom of an object makes a straight line.

Connect these lines with a straight line from the bottom to the top of an object and you have a triangle.

Another triangle is made by the top and bottom lines and a line from the top of the shadow to the bottom on a screen.

These triangles are similar triangles. See the Math Root below.

Math Root

A triangle of base length do and height ho is made by the point of light and an object.

A similar triangle is made by the point of light and the shadow of height hs and distance ds.

These are similar triangles. So hs/ho = ds/do

Questions

If the source of light is the sun so that do is huge, and since the distance from the object to the screen is much smaller do is approximately equal to ds. In this case, how does the size of the shadow depend on the distance between the object and the screen?

How the image was made.

The mage is the shadow of a person made on a vertical wall by the setting sun.

What else do you see in this image?

See the bottom of the page for an explanation.

For Monks

When the rays from the sun rise up at sunset they are known in English as "rays of Buddha".

Rays of light produced by the setting sun appear in the hazy air above Side Turkey.

Consider this image of the shadow of a tree on the ground. What is the true shape of the shadow?

The shadow of a tree on the ground. What is the true shape of the shadow?

The shadow of the person above seems to have a second dim shadow above the dark shadow. There must have been two light sources and yet there was only the sun.

The picture was taken at sunset, and there was a calm ocean behind the person.

The flat surface of the water acted like a mirror and made an image sun below the water which cast the second shadow.