Shadow within shadow

Answer to a question under the Science & Technology section of THE HINDU, 22^nd Jan 2009.

Question: When a smaller object (like a scooter) is in the shadow of a bigger object (like a tree) we still see its faint shadow in the larger object’s shadow in daylight. How is this possible?

http://www.hindu.com/seta/2009/01/22/stories/2009012250181500.htm

Rephrased Question:

How does a shadow appear for an object which is already in a shadow of another bigger object?

http://www.hindu.com/seta/2009/06/18/stories/2009061850201500.htm

The answer to your question lies in the question, if the scooter is to be in the shadow, then how is it visible in the first place? To answer these questions, we need to review the way in which light or any other EMR interacts with matter.

Light (or any EMR in general) on interaction with matter can either get transmitted, reflected or absorbed or all the above in different proportions. When a material does not transmit light through it, a region of darkness is formed to the side, opposite the source of light, called a shadow. This can happen only when there is a single source of light and the rays travel parallel like in a laser.

In the case under study, the light from sun gets multiply scattered (reflected in all directions) by the objects nearby the tree. These light rays hit the scooter and get reflected to the eyes of the observer, hence the scooter is visible. Some of these rays do fall on the shadowed portion of the tree too. In the same lines, since the scooter is another opaque body, it does not transmit light through it and hence casts a shadow, however of lesser intensity. We see this diffused shadow since the scooter obstructs the light (reflect from neighbouring objects) falling on the ground which would have otherwise happened. Since the light impinging on the scooter are from varied sources (scattered from nearby objects) and from different directions, the shadow is rather diffused and scarcely takes the outline of the scooter.

If the object in shadow (the scooter) were to receive the reflected light in equal amount from all directions (isotropic hemispherical irradiance) it would never cast a shadow. But in nature this can hardly occur and there would be one direction from which the reflected light is dominant. The smaller object (scooter) casts a shadow behind it in the direction of this source. In real time, the bigger object (tree) might cast its shadow in one direction, while the smaller object can cast another direction depending on the direction of dominant reflected light.

It is useful to recall that, objects like air, interact with light differently wherein they scatter and absorb minimally and transmit a larger percentage of incoming radiation and thus we do not see shadows of air. However we see shadows of clouds as they scatter away much of the incoming radiation while transmitting a little.