The aperture is the diameter of the opening of the lens.  Lenses usually have a variable iris to increase or decrease the opening inside the lens.  The aperture is indicated as an f/stop, or f/.  The smaller the value (2.8) more light comes in through the lens.  The larger the number (22), less light passes through the lens.

For example, you have a lens with a focal length of 50mm and it has a 25mm maximum opening inside the lens.  To determine the lens’ “speed” (maximum aperture) you divide the focal length by the largest diameter of the lens.  Using this example the formula is 50/25 = 2, which is a ratio of 2:1 or denoted as f/2. 

If the lens opening of the 50mm lens is 17.8mm, the f/stop would be determined as 50/17.8 = 2.8:1 or f/2.8.

If the lens opening of the 50mm lens is 12.5mm, the f/stop would be determined as 50/12.5 = 4:1 or f/4.

If the lens opening of the 50mm lens is 8.9mm, the f/stop would be determined as 50/8.9 = 5.6:1 or f/5.6.

The “ f/ ” refers to the mathematical function of the lens. 

The term “stop” originated from a time when lenses had no variable iris.  Small metal plates with different sized openings were placed inside the lens via a slot.  The original plates were called Waterhouse (the manufacturer) Stops as they “stopped” (reduced) light reaching the film.

Each time you increase the value of the f/stop by a whole stop, you are reducing the light reaching the recording medium by half.  If you allow more light into the lens by one full f/stop you double the amount of light going through the lens.  The smaller the f/stop number, the more light goes through the lens,  Ergo, f/2 allows more light through the lens than f/16.

So, what is a T/stop?

The T/stop is the actual amount of light that passes through a lens.  Its the TRUE stop of the aperture.

A lens may have the mathematical value of, for example, f/2.8, though due to the glass of the lens holding back some light the true value is actually the equivalent of f/3.1, or having a T/stop of T/3.1.

This is a value used in cinematic photography, where motion picture film exposure had and has to be correctly and exactly set.  Otherwise, motion picture film would usually be under exposed.

Each cinema lens has the amount of lens coming through it measured at each aperture and marked as T/stop.

In non-cinema photography the f/stop rating of the lens is usually close enough, and modern cameras have built-in meters that measure the actual amount of light coming through a lens.  Most cinema cameras do not have internal light meters, ergo T/stop is used.  A hand held meter may indicate f/6.3, you would set your lens to the T/6.3 mark.