Olive asked:

How is it possible to cast two shadows at the same time?

Answer by Craig Skinner

This looks like a science (optics) question rather than a philosophy one. But here’s the answer.

First, I presume you mean one object casting two shadows (two objects will obviously cast two shadows, one for each).

The usual way is to have two light sources, each casting a shadow. Thus, earlier tonight, I walked round the block. As I passed a street lamp, it cast my shadow in front of me, and the shadow lengthened as I walked on. As I neared the next lamp, it cast my shadow behind me, so now there were two, one behind and one in front of me. On a moonlit night, I can see three, one cast by each of the two lights, one by moonlight.

Less often, two shadows are cast even though there is only one light source. The usual explanation is that one shadow is cast directly by sunlight, the other by sunlight reflecting off a window. Very rarely, a thin band of dark cloud obscures a strip across the middle of the sun’s disc so that each unobscured bit of the disc acts as a separate light source and two shadows are cast, very slightly apart.

They say vampires casts no shadow. I’m sure this is true (because there are no vampires).

Finally there is a novel called ‘Casting Two Shadows’ which is well reviewed. I haven’t read it. I understand it is about love, honour and sacrifice, but tells us nothing about optics.

Answer by Geoffrey Klempner

In order to answer your question the first thing we need to decide is how you define a ‘shadow’.

A shadow can be a volume of space within which any partly or wholly contained object is described as being ‘in shadow’, or ‘in the shade’. The Earth’s shadow, in this sense, has the shape of a tapering cone, as the light source, the Sun, is larger than the Earth.

More often, we speak of a ‘shadow’ as a two dimensional shape on a surface. It is actually possible, to cast two shadows in this sense with one object and a compact light source, no mirrors, etc.

Let’s say I am walking across a bridge with an iron railing. I see my moving shadow cast by the sun on the iron railing, but I also see, in the distance, the shadow of the bridge on the meadow below, with the iron railing and my shadow. There are two shadows – two ‘two-dimensional shapes on a surface’ – one of which (from my viewpoint) is contained within the other.

However, in the first sense of ‘shadow’ there is only one shadow, i.e. one volume of space where the light from the sun cannot directly reach because I am in the way.