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This ratio is related to the image-space numerical aperture when the lens is focused at infinity. [3] Based on the diagram at the right, the image-space numerical aperture of the lens is:

Characteristic of an optical system The numerical aperture with respect to a point P depends on the half-angle, θ 1, of the maximum cone of light that can enter or exit the lens and the ambient index of refraction. As a pencil of light goes through a flat plane of glass, its half-angle changes to θ 2. Due to Snell's law, the numerical aperture remains the same:NA i = N w = ( 1 − m P ) N , {\displaystyle {\frac {1}{2{\text{NA}}_{\text{i}}}}=N_{\text{w}}=\left(1-{\frac {m}{P}}\right)N,} In laser physics, numerical aperture is defined slightly differently. Laser beams spread out as they propagate, but slowly. Far away from the narrowest part of the beam, the spread is roughly linear with distance—the laser beam forms a cone of light in the "far field". The relation used to define the NA of the laser beam is the same as that used for an optical system,

NA i = n sin ⁡ θ = n sin ⁡ [ arctan ⁡ ( D 2 f ) ] ≈ n D 2 f , {\displaystyle {\text{NA}}_{\text{i}}=n\sin \theta =n\sin \left[\arctan \left({\frac {D}{2f}}\right)\right]\approx n{\frac {D}{2f}},} Increasing the magnification and the numerical aperture of the objective reduces the working distance, i.e. the distance between front lens and specimen.In microscopy, NA is important because it indicates the resolving power of a lens. The size of the finest detail that can be resolved (the resolution) is proportional to λ / 2NA, where λ is the wavelength of the light. A lens with a larger numerical aperture will be able to visualize finer details than a lens with a smaller numerical aperture. Assuming quality ( diffraction-limited) optics, lenses with larger numerical apertures collect more light and will generally provide a brighter image, but will provide shallower depth of field. n sin ⁡ θ max = n core 2 − n clad 2 , {\displaystyle n\sin \theta _{\max }={\sqrt {n_{\text{core}} Numerical aperture is not typically used in photography. Instead, the angular aperture of a lens (or an imaging mirror) is expressed by the f-number, written f/ N, where N is the f-number given by the ratio of the focal length f to the diameter of the entrance pupil D: