Relative aperture (or lens speed) is ability of the lens to give more or less bright image on the film at same conditions. Larger relative aperture allows shooting at lower light levels. Used aperture also affects depth of field.
There are two different relative apertures - geometrical и effective.
Geometrical relative aperture value is determined by maximum diameter of the focal aperture and focal length as
where D - maximum focal aperture diameter, F - focal length.
Focal aperture is image of the aperture diaphragm through the lens part in front of it. In most lenses focal aperture in fully opened state is almost equal to diameter of the front glass element. Excludes from this rule are super-wide lenses that have front element much larger that focal aperture.
When the geometric aperture value is determined, no light loses due to reflection and absorption are considered. So, actual lens speed (effective relative aperture) is always smaller than geometrical one by value of all light loses in the lens. In complex lenses with many glass elements, such loses may be about 30-40%, and they should be considered for exposure calculation. That is why all modern movie lenses have aperture scale marked in values of the effective apertures. Value of the geometrical aperture is marked on the front ring of the lens housing. Some foreign lenses have aperture scales marked in both geometrical and effective aperture values. In this case, effective aperture values are marked with red paint, whereas values of the geometrical aperture are marked with white paint.
To reduce light loses and to increase image contrast, all modern lenses have coated elements. This means that surfaces of the elements bordering with air are covered with this transparent material that has average refraction ratio between glass and air. Such film reduce amount of reflected light significantly that causes more light to pass through the lens, and less light is being dispersed.
Best performance is possible when thickness of the coating is equal to ј of the light wave length. This condition can be true for a single wave length only, so it is impossible to eliminate reflections completely.
The plot below shows relation of the reflected light amount of a single glass/air border before and after coating. As you can see, reflection is eliminated completely for the single wave length only (λ=560мμ in this case), but reduced significantly for other wave lengths as well.
In accordance with USSR GOST, diaphragm scales of lenses are marked in the effective aperture values. Series of the marked values is set so the each following aperture mark corresponds to double or half light amount passed through the lens compared to preceding mark. Amount of the transmitted light is directly proportional to the area of the aperture opening, so suitable relative aperture values are 1:1, 1:1.4; 1:2; 1:2.8; 1:4; 1:5.6; 1:8; 1:11; 1:16; 1:22.
First mark of the aperture scale lens corresponds to the value of the full opened diaphragm, and it may differ from the series mentioned above. All other values should match the specified row. Second mark may be without inscription if it's value differs from the first mark less that 10%.
For user's convenience, aperture values are marked with their denominators only - 1, 1.4; 2; 2.8; 4; 5.6 etc.