A shoot-through umbrella works very simply by taking the light from a light source and expanding it’s spread.
A shoot-through umbrella is typically white and a fairly thin or translucent white at that. The light is intended to travel through the umbrella to reach it’s subject.
To show you exactly I’ve put together some diagrams that show where the light goes. For this example we’ll assume that an umbrella is a cut of a perfect sphere. The focal point, through which all the reflected light passes, is 1/2 * radius of the circle, or half way between the sphere’s center point and the edge of the umbrella.
When the light hits the reflective surface it bounces both through the umbrella and some spill (usually about 1f stop) comes back in a straight line through the focal point. The light that gets through the umbrella’s surface travels in the opposite direction of the light that reflects back from the umbrella’s surface.
You can see where the reflected light hits the subject.
At first you’d expect to want to place your subject at the tip of the umbrella (like shown in the diagram) but that’s rarely the best idea – we’ll cover that in another article.