Shadows and Eclipses

1Sharp or fuzzy?

Hold your hand under a single bright LED torch and its shadow on the desk has sharp edges. Hold it under a long fluorescent tube in the classroom ceiling and the shadow is fuzzy: dark in the middle and grey at the edges. On a cloudy afternoon your shadow almost disappears. All of these follow from one fact you met in lesson 1: light travels in straight lines, and an opaque object blocks the rays that hit it.

2A point source: a sharp shadow

Figure 2.1: A point source. Every point on the screen either receives light from the source or does not, so the shadow is all umbra, with sharp edges.

To find the shadow, draw straight rays from the source past the top and bottom edges of the object to the screen. The shadow lies between them. The rays spread out, so the shadow is bigger than the object; the triangles formed by the rays are similar, so

3An extended source: umbra and penumbra

Figure 2.2: An extended source. The solid rays mark the umbra; the dashed rays, from each edge of the source past the opposite edge of the object, mark the outer edge of the penumbra.

A frosted bulb, a fluorescent tube or the Sun is an extended source: light comes from many points across its surface. Near the middle of the screen, no part of the source can be seen past the object: that is the umbra. Towards the edges, some of the source is hidden and some is not: that is the penumbra, which gets lighter towards its outer edge.

4Eclipses: shadows in space

The Sun lights the Earth and the Moon, and each of them casts a long shadow into space, with an umbra and a penumbra because the Sun is an extended source. An eclipse happens when the Sun, the Earth and the Moon are in a straight line, so that one of them moves into the shadow of another.

Figure 2.3: A solar eclipse (not to scale). People in the Moon's umbra see a total eclipse; people in its penumbra see a partial eclipse.

The Moon's umbra is only just long enough to reach the Earth, so a total solar eclipse is seen only along a narrow path, usually less than about $250\mathrm{k}\mathrm{m}250\backslash ,\backslash mathrm\{km\}$ wide, and lasts only a few minutes at any one place. Over a much wider region, in the penumbra, people see a partial eclipse: a "bite" taken out of the Sun. Sometimes the Moon is a little further from the Earth and its umbra does not reach us at all; then a bright ring of Sun is left round the Moon, an annular eclipse.

Figure 2.4: A lunar eclipse (not to scale). The Earth's umbra is wide enough to swallow the whole Moon.

A lunar eclipse can be seen from everywhere on the night side of the Earth, and totality can last well over an hour. The Moon does not disappear: a little sunlight is bent through the Earth's atmosphere into the umbra, and it lights the Moon a dull red. The total lunar eclipse of 27 July 2018, the longest of this century, was seen clearly across East Africa, including Rwanda.