Binoculars consist of a pair of telescopes that are mounted next to each other. Each eye uses one of the telescopes to view an image that is not only magnified but also gives the appearance of depth when the lenses are properly aligned. The exact magnification that a binocular provides may be calculated from the focal length of the objective lens and eyepiece. However, in practice, the magnification relies almost exclusively on the diameter of the objective lens.
Define magnification. This is the ratio of the apparent size of an object to its actual size and is therefore a pure number without units. A hand-held pair of binoculars typically has a magnification of 7 to 12. Higher magnifications are technically possible but require the binoculars to be mounted securely.
Measure the objective lens. This is the lens at the front of the binoculars that gathers the light and affects the potential magnification of the binoculars. The objective lens on a pair of binoculars is typically about 50 mm in diameter.
Calculate the focal length of the lens. This depends on the physical properties of the lens, but it is typically at least 4 times the width of the lens. The focal length of the lens for a pair of binoculars is therefore 200 to 250 mm.
Obtain the focal length of the eyepiece. The diameter of the eyepiece should be about the diameter of a fully dilated human pupil, about 7 mm. The focal length of the eyepiece is therefore about 25 mm.
Calculate the magnification of the binoculars. This can be given as MA = fo/fe where "fo" is the focal length of the objective lens and "fe" is focal length of the eyepiece. This shows that MA = 200/25 = 8 for most binoculars. Note that the magnification of a pair of binoculars generally relates directly to the size of the objective lens, since the size of the eyepiece is more or less fixed to the diameter of a fully dilated pupil.