Dimensionless number in the context of "Bulk Richardson Number"

An f-number is a measure of the light-gathering ability of an optical system such as a camera lens. It is defined as the ratio of the system's focal length to the diameter of the entrance pupil ("clear aperture"). The f-number is also known as the focal ratio, f-ratio, or f-stop, and it is key in determining the depth of field, diffraction, and exposure of a photograph. The f-number is dimensionless and is usually expressed using a lower-case hooked f with the format f/N, where N is the f-number.

The f-number is also known as the inverse relative aperture, because it is the inverse of the relative aperture, defined as the aperture diameter divided by the focal length. A lower f-number means a larger relative aperture and more light entering the system, while a higher f-number means a smaller relative aperture and less light entering the system. The f-number is related to the numerical aperture (NA) of the system, which measures the range of angles over which light can enter or exit the system. The numerical aperture takes into account the refractive index of the medium in which the system is working, while the f-number does not.

In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface (e.g., a flat interface). The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective (and hence its light-gathering ability and resolution), and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along it.

The scale ratio of a model represents the proportional ratio of a linear dimension of the model to the same feature of the original. Examples include a 3-dimensional scale model of a building or the scale drawings of the elevations or plans of a building.

In such cases the scale is dimensionless and exact throughout the model or drawing.

John William Strutt, 3rd Baron Rayleigh (/ˈreɪli/ RAY-lee; 12 November 1842 – 30 June 1919), was a British physicist and hereditary peer who received the Nobel Prize in Physics in 1904 for his discovery of argon.

Rayleigh provided the first theoretical treatment of the elastic scattering of light by particles much smaller than the light's wavelength, a phenomenon now known as Rayleigh scattering, which notably explains why the sky is blue. He studied and described transverse surface waves in solids, now known as Rayleigh waves. He contributed extensively to fluid dynamics, with concepts such as the Rayleigh number (a dimensionless number associated with natural convection), Rayleigh flow, the Rayleigh–Taylor instability, and Rayleigh's criterion for the stability of Taylor–Couette flow.

In epidemiology, the basic reproduction number, or basic reproductive number (sometimes called basic reproduction ratio or basic reproductive rate), denoted ${\displaystyle R_{0}}$ (pronounced R nought or R zero), of an infection is the expected number of cases directly generated by one case in a population where all individuals are susceptible to infection. The definition assumes that no other individuals are infected or immunized (naturally or through vaccination). Some definitions, such as that of the Australian Department of Health, add the absence of "any deliberate intervention in disease transmission". The basic reproduction number is not necessarily the same as the effective reproduction number ${\displaystyle R}$ (usually written ${\displaystyle R_{t}}$ [t for "time"], sometimes ${\displaystyle R_{e}}$), which is the number of cases generated in the current state of a population, which does not have to be the uninfected state. ${\displaystyle R_{0}}$ is a dimensionless number (persons infected per person infecting) and not a time rate, which would have units of time, or units of time like doubling time.

${\displaystyle R_{0}}$ is not a biological constant for a pathogen as it is also affected by other factors such as environmental conditions and the behaviour of the infected population. ${\displaystyle R_{0}}$ values are usually estimated from mathematical models, and the estimated values are dependent on the model used and values of other parameters. Thus values given in the literature only make sense in the given context and it is not recommended to compare values based on different models. ${\displaystyle R_{0}}$ does not by itself give an estimate of how fast an infection spreads in the population.

In physics, a dimensionless physical constant is a physical constant that is dimensionless, i.e. a pure number having no units attached and having a numerical value that is independent of whatever system of units may be used.

The concept should not be confused with dimensionless numbers, that are not universally constant, and remain constant only for a particular phenomenon. In aerodynamics for example, if one considers one particular airfoil, the Reynolds number value of the laminar–turbulent transition is one relevant dimensionless number of the problem. However, it is strictly related to the particular problem: for example, it is related to the airfoil being considered and also to the type of fluid in which it moves.