A magnifying glass (called a hand lens in laboratory contexts) is a convex lens made of glass or PMMA plastic (pretty much as good as glass) that is used to produce a magnified image of an object. The lens is most commonly known mounted in a frame with a handle but can also be mounted in desk stands, eyeloupes, linen testers, spectacles and numerous other formats. Some are illuminated by bulbs tubes or LEDs.
A sheet magnifier consists of many very narrow concentric ring-shaped lenses, such that the combination acts as a single lens but is much thinner. This arrangement is known as a Fresnel lens, they are often used for magnifying large areas, albeit with less image quality than conventional glass or PMMA lenses.
An electronic magnifier uses a combination of a lens, a camera and a display. This overcomes many limitations of conventional magnifiers because high magnifications can be achieved with a larger view and high magnification images can be comfortably viewed at a distance.
Microscopes are the ultimate magnifier and are often more useful, albeit more expensive, for higher magnification observations, microscopes have an optical magnification range from 2x to 1600X, there being a huge variety of different types. We are experts in microscopy and can readily assst you in your selection.
The earliest evidence of "a magnifying device, a convex lens forming a magnified image" was Aristophanes's "lens", from 424 BC, a glass globe filled with water. (Seneca wrote that it could be used to read letters "no matter how small or dim"). Roger Bacon described the properties of a magnifying glass in 13th-centuryEngland. Eyeglasses were developed in 13th-century Italy.
The magnification of a magnifying glass depends upon where it is placed between the user's eye and the object being viewed, and the total distance between them. The magnifying power is equivalent to angular magnification (this should not be confused with optical power, which is a different quantity). The magnifying power is the ratio of the sizes of the images formed on the user's retina with and without the lens.
For the "without" case, it is typically assumed that the user would bring the object as close to the eye as possible without it becoming blurry. This point, known as the near point, varies with age. In a young child it can be as close as 5 cm, while in an elderly person it may be as far as one or two metres. Magnifiers are typically characterized using a "standard" value of 0.25 m.
The higher the magnification you want, the smaller will be the lens - an immutable fact. Also the distance from the subject will get shorter and the distance of the magnifier to the eye also becomes shorter. Only an electronic magnifier can overcome these physical restrictions
The highest magnifying power is obtained by putting the lens very close to the eye and moving the eye and the lens together to obtain the best focus. The object will then typically also be close to the lens. The magnifying power obtained in this condition is MP0 = ¼Φ + 1, where Φ is the optical power in dioptres, and the factor of ¼ comes from the assumed distance to the near point (¼ m from the eye). This value of the magnifying power is the one normally used to characterize magnifiers. It is typically denoted "m×", where m = MP0. This is sometimes called the total power of the magnifier (again, not to be confused with optical power).
Magnifiers are not always used as described above, however. It is much more comfortable to put the magnifier close to the object (one focal length away). The eye can then be a larger distance away, and a good image can be obtained very easily; the focus is not very sensitive to the eye's exact position. The magnifying power in this case is roughly MP = ¼Φ.
A typical magnifying glass might have a focal length of 25 cm, corresponding to an optical power of 4 dioptres. Such a magnifier would be sold as a "2×" magnifier. In actual use, an observer with "typical" eyes would obtain a magnifying power between 1 and 2, depending on where lens is held.
Using this principle, a magnifying glass can also be used to focus light, such as to concentrate the sun's radiation to create a hot spot at the focus.
Higher magnifications give a narrower depth of focus.
Magnifying glasses typically have low magnifying power: 2×–6×, with the lower-power types being much more common. At higher magnifications, the image quality of a simple magnifying glass becomes poor due to optical aberrations, particularly spherical aberration. When more magnification or a better image is required, other types of hand magnifier are typically used. High power magnifiers are sometimes mounted in a cylindrical or conical holder with no handle. This is called a loupe.
Such magnifiers can reach up to about 30×, and at these magnifications the aperture of the magnifier becomes very small and it must be placed very close to both the object and the eye. For more convenient use or for magnification beyond about 30×, one must instead use a microscope.
References: Cambridge Optics knowledgebase, wikipaedia, optical institute & assorted contributors