Shadows
The shadow knows
The size of a shadow depends not only on the size of the object casting the shadow but also on the position of the light source and screen.

Unscrew the front of the Maglite. It will turn on. Continue to unscrew the front until it comes off completely. Slip the removed front onto the back of the flashlight. The flashlight will then stand up on a table. Place a white screen on the table about 1 meter from the light.

Put your fingers between the light and the screen. Make shadows. Can you make the shadow of a rabbit? Move your hand toward the screen and away from the screen and notice how the shadow changes size. The shadow gets large when your hand approaches the light. Notice the sharp edges of the shadow. Replace your hand with a cardboard cutout.

Light travels in straight lines. The straight lines go from the point of light to the edge of the object and continue to the screen. So when the object is close to the light it makes a large shadow. The shadow has sharp edges because the light source is small.

So What?
On a clear dark, moonless, morning or evening Venus shines bright enough to cast a shadow of your hand onto a white surface. Notice how the shadow of your hand remains sharp edged and does not change size as you move you hand toward and away from the white screen. The distance from your hand to the small point source of Venus does not change much (at least percentagewise) as you move your hand toward and away from the screen, so the size of the shadow does not change much either.
Math Root
Measure the width of the shadow, S, the width of the cardboard cutout, C, the distance from the light to the cardboard, D, and the distance from the light to the wall, L.



Compute and compare the ratios S/L and C/D
Since the lengths in these ratios are corresponding sides of similar triangles the ratios should be equal.

By
Paul Doherty