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Power : Power means the degree to which the subject being looked at is magnified or enlarged. A 10x power means that you are magnifying something 10 times. Say you are looking at a tree that is 100m away. With a 10x binocular it would look ten times closer (or, only 10m away). The greater the power, the smaller the field of view, and in general the lower the brightness of the image.
Occular : The Occular lens is the lens that is closest to your eyes when you hold a pair of binoculars up to look through (the smallest lens).
Objective Lens : The objective lens is the lens at the other end (the larger lens). It's purpose is to gather light from a sharply focused image of a distant subject. The larger the objective, the more light it gathers, all else being equal. Conversely, the smaller the objective, the lighter weight and more compact the unit will be - an important factor in back packing, etc.
Exit Puple : The most important number associated with binoculars is actually the exit puple It is the diameter of the beam (in mm) that leaves the eyepiece. The larger the exit pupil, the brighter the image. and the better they are for viewing things in low light situations (like dawn or dusk). The exit pupil is calculated by dividing the diameter of the objective lens by the power (objective diameter/power). Exit pupils of 6-7mm are generally found in "night glasses, while exit pupils of 4-5mm are found in general purpose binoculars.
Relative Brightness : The term relative brightness refers to how much light a binocular gathers. It is calculated by squaring the exit pupil (objective diameter/power)². If the optics are fully-coated the relative brightness is increased by 50%.
Field of View : Field of view is the width of the the viewing area seen through the binoculars - it decreases as magnification increases. It is expressed in degrees and also in feet. A 7x50 binocular may include 7.1º and include 375 feet at 100 yards.
Porro-Prism : Binoculars with porro-prisms have the traditional binocular shape with the eyepiece offset from the objective lenses on each side.
Roof prisms : Roof Prism binoculars feature in-line optics, and are lighter, more compact, but generally cost more.
Lens Coating : Lenses can be coated to increase the transmission of light. Fully-coated (FC) means all the air-glass surfaces are coated. Multi-coated (MC) means that one or more surfaces, of one or more lenses, have been coated with multiple layers. Fully Multiple-coated (FMC) means that all air-glass surfaces have multiple layers of coating. Uncoated glass will waste about 6% of all the light that strikes it , meaning that an uncoated binocular will throw away over half the light coming in to an objective.
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Fixed some typing errors.