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For example, if you're in a room with a light bulb on the ceiling, the closer your hand is to the wall, the more defined the shadow of your hand will be.

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There are two factors that cause a shadow to have blurred edges which get sharper the shorter the distance between the object causing it and the surface upon which it falls.

One factor is diffraction, which causes light to spread when it passes an edge.

The other factor, which will be the dominant one with typical light sources in the home, is that the light does not emanate from a point but from a wider area- for example, a regular incandescent bulb might be a couple of inches in diameter. That means that there will be an area around the edge of the shadow in which the object has blocked the light from one side of the source but not from the other. That area is known as the pen-umbra, while the darker central part of a shadow, where the object blocks light from across the full width of the source, is known as the umbra. The pen-umbra is a angular distribution of gradually fading intensity, so the nearer the object is to the surface the less opportunity there is for the pen-umbra to spread.

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Reflection: light reflects off surfaces. If you are far away from the wall, light can still arrive at the wall by reflecting off other walls. Therefore your shadow is both 1) not as dark and 2) relatively indistinct. If you are close to it, then much of this reflected light is blocked, and you get a sharper shadow.

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This is not generally true. If the light comes from a single point then the shadow is sharp. The further away your hand is form the light source the better it may resemble a point source. The effect of the light source extension, better known as h as lf shadow, is larger the further your hand is from the wall.

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This is due to the diffraction (not reflection) of lightwaves at the edges of your hand. Diffraction is the spreading of waves eg. from an edge. The refracted wave spread out as it pass your hand, and the smearing of your hand is therefore bigger when the light travels a long distance after your hand.

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