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Hereof, what does 40x zoom mean?
Its 40x optical lens means it can capture from an equivalent 24mm wide-angle (wide enough for shots of groups, say, or landscapes), through to a massive 960mm equivalent (long enough to pick out far-away subjects and make them appear close-up within the frame).
Similarly, how does a zoom lens work? An optical zoom lens works the same way as any other lens, except it has a system with moveable glass pieces that can shift around to give the lens different focal lengths. When you change the focal length it also changes the field of view of the image.
In this way, what does 50x zoom mean?
In terms of cameras (and also binoculars and telescopes), the 50x (or whatever) is zoom range from the starting value (x). So if a zoom lens is 18–300 mm, then it is said to have a zoom or (more correctly) magnification 16.67x factor. In a telescope there is no zoom lens.
What is a 300mm zoom equivalent to?
At 300mm the lens will have the equivalence of a 450mm lens on a 35mm film camera or Nikon FX (Full Frame) digital camera. Many P&S cameras will say they have a 8x or 12x zoom, that just means that the longest focal length is 8x or 12x longer than the widest focal length.