Light travels in straight lines: shadows

In a total solar eclipse the dark centre of the Moon’s shadow often covers a strip less than 50 miles wide, while the partial shadow spans a thousand miles or more.

Rays: a simple model of light

Sunlight through a gap in the curtains makes a beam with straight edges, and a torch beam in fog is a straight cone. In a material of the same kind all the way through, light goes in straight lines. Optics uses this to draw light as rays: straight lines with arrows showing which way the light moves. OpenStax calls this part of the subject geometric optics. The ray picture works well as long as the objects the light meets are much larger than its wavelength, which for visible light is less than a micrometre. Mirrors, lenses, cameras and shadows all fall into that range.

We see a lamp because rays from it enter our eyes. We see a book because rays from the lamp hit the book and bounce off in all directions, and some of those rays reach us. Our eyes and brain then assume the light came in a straight line, and place the object back along that line. Most of the time this assumption is right. When it is wrong, for instance when light bends at the surface of water, we see things in places where they are not, which is the subject of a later lesson.

Pinholes and upside-down pictures

A box with a tiny hole in one side and a screen on the other makes a picture without any lens. A ray from the top of a tree can only reach the screen by passing through the hole, so it lands near the bottom of the screen; a ray from the bottom of the tree lands near the top. The picture is upside down. Its size follows from similar triangles: image height ÷ object height = box depth ÷ object distance. A 10 m tree 20 m away seen in a box 10 cm deep makes an image 10 × 0.1 ÷ 20 = 0.05 m, or 5 cm, tall. Darkened rooms with a small hole, called camera obscura, were used by scientists such as Kamal al-Din al-Farisi in his studies of light in the early 1300s, as OpenStax describes.

Sharp shadows and soft shadows

A shadow is the region behind an opaque object that light cannot reach in a straight line. With a very small light source, a point source, every place is either fully lit or fully dark, and the shadow has a sharp edge. Its size again follows from similar triangles. A 4 cm ball 20 cm from a point lamp casts a shadow 4 × 50 ÷ 20 = 10 cm across on a screen 50 cm from the lamp. Move the ball toward the lamp and the shadow grows; move it toward the screen and the shadow shrinks toward the size of the ball.

Most real lights are not points. With a lamp of some size, some places on the screen are hidden from the whole lamp and others from only part of it. The fully dark centre is the umbra, and around it is a lighter ring, the penumbra, where part of the lamp can still be seen. Straight lines from the edges of the lamp past the edges of the object mark the boundaries. The bigger the lamp and the farther the screen, the wider the penumbra and the smaller the umbra; if the lamp is large enough, the umbra disappears entirely and the shadow is soft all over.

Eclipses: shadows in space

The Sun is a large source, so the Moon and the Earth cast shadows with both an umbra and a penumbra. NASA explains that in a solar eclipse, observers inside the small umbra see the Sun completely blocked, a total eclipse, while those in the much larger penumbra see only part of the Sun covered. As the shadow extends away from the Moon, the umbra narrows, so by the time it reaches the Earth it covers a small area: NASA gives a typical umbral path as less than 50 miles wide, against a penumbra a thousand miles or more across. In a lunar eclipse the Moon passes into the Earth’s shadow instead. Some sunlight bent through the Earth’s atmosphere still reaches it, mostly red, which gives the eclipsed Moon its reddish colour.