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What factors affects the size of a shadow and how would you derive the diameter of a shadow of a circular object on a flat screen?

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It's based on the distance and orientation of the light source, whether it becomes an ellipse or a larger circle ;-) – Waffle's Crazy Peanut May 30 '13 at 13:19
If the light source isn't pointlike, the shadow doesn't have sharp edges. – Ben Crowell May 30 '13 at 15:36

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up vote 2 down vote accepted

Instead of the Circular object I use a cardboard with a circular cavity that will behave same as the object, instead the lighted portion on screen would be shadow in that case :)

enter image description here

$$\tan\theta=\dfrac r d =\dfrac R{d+D} $$

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