How do I calculate the size of a shadow

High School Dude

13th August 2006 - 01:37 PM

For my science homework, I have to calculate the size of a shadow on a screen.
The object is a vertical pencil 15cm high which is 30cm away from a small spotlight which is almost level with the pencil. The screen is 1m away from the spotlight.

Please, I need help. Is there some sort of formula for calulating the size of a shadow formed by a certain object aginst a screen.

rpenner

13th August 2006 - 07:14 PM

Think about triangles. Light spreads in straight lines, so the source of the light is in a straight line with all of shadows of the top of the pencil. Also, the source of the light is in a straight light with all of the shadows of the bottom of the pencil. So if the screen and the pencil are parallel, we have a situation of similar triangles. Therefore the problem reduces to one of units and ratios.

CODE

+---------+ X / 1 m (at screen)
| /
| /
| /
| /
+----+ 15 cm / 30cm (at pencil)
| /
| /
| /
|/
+ source

X = 1 m * 15 cm / 30 cm = 100 cm * 1/2 = 50 cm.

Image by photoshop, copyright 2006 by Triangle Technologies Inc.

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