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Normal optical microscopes can magnify up to 1500× with a theoretical resolution of 0.2 μm . The lenses can be quite complicated and are composed of multiple elements to reduce aberrations. Microscope objective lenses are particularly important as they primarily gather light from the specimen. Three parameters describe microscope objectives: the numerical aperture (NA) , the magnification ( m ) size 12{ \( m \) } {} , and the working distance. The NA is related to the light gathering ability of a lens and is obtained using the angle of acceptance θ size 12{θ} {} formed by the maximum cone of rays focusing on the specimen (see [link] (a)) and is given by

NA = n sin α, size 12{ ital "NA"=n"sin"α} {}

where n size 12{n} {} is the refractive index of the medium between the lens and the specimen and α = θ / 2 size 12{α= {θ} slash {2} } {} . As the angle of acceptance given by θ size 12{θ} {} increases, NA becomes larger and more light is gathered from a smaller focal region giving higher resolution. A 0 . 75 NA size 12{0 "." "75" ital "NA"} {} objective gives more detail than a 0 . 10 NA size 12{0 "." "10" ital "NA"} {} objective.

Part a of the figure shows a horizontal dotted line, a point P on the line and an objective lens at a distance from the point such that a triangle is formed from point P to the edges of the lens. An angle theta is shown at point P, representing the maximum cone of rays entering the lens from point P. Part b of the figure shows light rays from a specimen entering a camera lens held above it. The rays form an inverted cone.
(a) The numerical aperture (NA) of a microscope objective lens refers to the light-gathering ability of the lens and is calculated using half the angle of acceptance θ . (b) Here, α is half the acceptance angle for light rays from a specimen entering a camera lens, and D is the diameter of the aperture that controls the light entering the lens.

While the numerical aperture can be used to compare resolutions of various objectives, it does not indicate how far the lens could be from the specimen. This is specified by the “working distance,” which is the distance (in mm usually) from the front lens element of the objective to the specimen, or cover glass. The higher the NA size 12{ ital "NA"} {} the closer the lens will be to the specimen and the more chances there are of breaking the cover slip and damaging both the specimen and the lens. The focal length of an objective lens is different than the working distance. This is because objective lenses are made of a combination of lenses and the focal length is measured from inside the barrel. The working distance is a parameter that microscopists can use more readily as it is measured from the outermost lens. The working distance decreases as the NA size 12{ ital "NA"} {} and magnification both increase.

The term f / # size 12{ {f} slash {#} } {} in general is called the f size 12{f} {} -number and is used to denote the light per unit area reaching the image plane. In photography, an image of an object at infinity is formed at the focal point and the f size 12{f} {} -number is given by the ratio of the focal length f size 12{f} {} of the lens and the diameter D size 12{D} {} of the aperture controlling the light into the lens (see [link] (b)). If the acceptance angle is small the NA size 12{ ital "NA"} {} of the lens can also be used as given below.

f /# = f D 1 2 NA . size 12{f"/#"= { {f} over {D} } approx { {1} over {2 ital "NA"} } } {}

As the f size 12{f} {} -number decreases, the camera is able to gather light from a larger angle, giving wide-angle photography. As usual there is a trade-off. A greater f / # size 12{ {f} slash {#} } {} means less light reaches the image plane. A setting of f / 16 size 12{ {f} slash {"16"} } {} usually allows one to take pictures in bright sunlight as the aperture diameter is small. In optical fibers, light needs to be focused into the fiber. [link] shows the angle used in calculating the NA size 12{ ital "NA"} {} of an optical fiber.

Practice Key Terms 4

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Source:  OpenStax, Selected chapters of college physics for secondary 5. OpenStax CNX. Jun 19, 2013 Download for free at http://legacy.cnx.org/content/col11535/1.1
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