Monocular

A monocular is a modified refracting telescope used to magnify the images of distant objects by passing light through a series of lenses and usually prisms, the application of prisms resulting in a lightweight, compact telescope. The typical volume and weight of a monocular are less than half of a pair of binoculars having similar optical properties, making a monocular easier to carry, and also proportionally less expensive. This is due to the fact that monoculars typically only have half the optics of binoculars, as they only process 1 image as opposed to 2. Monoculars produce 2-dimensional images, while binoculars add perception of depth (3 dimensions), assuming one has normal binocular vision.
Monoculars are ideally suited to those with vision in only one eye, or where compactness and low weight are important (e.g. hiking). Monoculars are also sometimes preferred where difficulties occur using both eyes through binoculars because of significant eye variation or poor vision in one eye.
A monocular with a straight optical path is relatively long; prisms are normally used to fold the optical path to make an instrument which is much shorter (see the entry on binoculars for details).
Visually impaired people may use monoculars to see objects at distances at which people with normal vision do not have difficulty, e.g., to read text on a chalkboard or projection screen. Applications for viewing more distant objects include natural history, hunting, marine and military. Compact monoculars are also used in art galleries and museums to obtain a closer view of exhibits.
When high magnification, a bright image, and good resolution of distant images are required, a relatively larger instrument is preferred (i.e. a telescope), often mounted on a tripod. A smaller pocket-sized "pocket scope" (i.e. a typical monocular) can be used for less stringent applications. These comments are quantified below.
Whereas there is a huge range of binoculars on the world market, monoculars are less widely available and with a limited choice in the top quality bracket, with some traditionally very high quality optical manufacturers not offering monoculars at all. Today, most monoculars are manufactured in Japan, China, Russia and Germany, with China offering more product variety than most. Prices range widely, from the highest specification designs listed at over £300 down to "budget" offerings at under £10. (As at February 2016).
Monocular sizes.
As with binoculars and telescopes, monoculars are primarily defined by two parameters: magnification and objective lens diameter, for example, 8×30 where 8 is the magnification and 30 is the objective lens diameter in mm (this is the lens furthest from the eye). An 8× magnification makes the distant object appear to be 8 times larger at the eye. Contemporary monoculars are typically compact and most normally within a range of 4× magnification to 10×, although specialized units outside these limits are available. Variable magnification or zoom is sometimes provided, but has drawbacks and is not normally found on the top quality monoculars. Objective lens diameter is typically in the range 20mm to 42mm. Care is needed in interpreting some monocular specifications where numerical values are applied loosely and inaccurately—e.g. "39×95", which on a small cheap monocular is more likely to refer to the physical dimensions than the optical parameters. (This is covered in more detail in the section "Interpreting product specifications" below.)
As with binoculars, possibly the most common and popular magnification for most purposes is 8×. This represents a usable magnification in many circumstances and is reasonably easy to hold steady without a tripod or monopod. At this magnification, the field of view is relatively wide, making it easier to locate and follow distant objects. For viewing at longer distances, 10× or 12× is preferable if the user is able to hold the monocular steady. However, increasing magnification will compromise the field of view and the relative brightness of the object. These and other considerations are major factors influencing the choice of magnification and objective lens diameter. Although very high numerical magnification sounds impressive on paper, in reality, for a pocket monocular it is rarely a good choice because of the very narrow field of view, poor image brightness and great difficulty in keeping the image still when hand holding. Most serious users will eventually come to realise why 8× or 10× are so popular, as they represent possibly the best compromise and are the magnifications most commonly adopted in the very highest quality field monoculars (and binoculars).
Where a monocular ends and a telescope starts is debatable but a telescope is normally used for high magnifications (>20×) and with correspondingly larger objective lens diameter (e.g. 60–90mm). A telescope will be significantly heavier, more bulky and much more expensive than a monocular and due to the high magnifications, will normally need a tripod, telescopes used for astronomy typically have inverted images. Most popular monocular sizes mimic popular binoculars – e.g. 7×25, 8×20, 8×30, 8×42, 10×42.
Design.
Much of the basic design considerations and related parameters are the same as for binoculars and are covered in that entry, but some expanded comments have been added where appropriate:
Exit pupil is defined as the diameter of the objective lens divided by the magnification and expressed in mm. (e.g. a 8×40 will give an exit pupil diameter of 5mm). For a given situation, the greater the exit pupil, the better the light transmission into the eye. Hence a large objective lens with a low magnification will give good light admission, especially important in deteriorating light conditions. The classic 7×50 marine binocular or monocular is ideally suited to low light conditions with its relatively large exit pupil diameter of 7.1mm and a realistic magnification which is practical on a moving boat. However, the exit pupil should be considered in relationship with the human eye pupil diameter. If the exit pupil of the chosen instrument is greater than the human eye pupil then there will be no benefit, as the eye will be the limiting factor in light admission. In effect, the extra light-gathering potential is wasted. This is a consideration as one ages, because human eye pupil dilation range diminishes with age, as shown as an approximate guide in the table below.
Field of view (fov) and magnification are related; for a given situation, fov increases with decreasing magnification and vice versa. This applies to monoculars, binoculars and telescopes. However, this relationship also depends on optical design and manufacture, which can cause some variation. The chart below has been compiled by the author to show the fov/magnification relationship based on best-in-class data, taken both from personal tests and from manufacturers' specifications. Contrary to some belief, it is a myth that binoculars offer a wider field of view than monoculars. For a given specification and manufacturer offering both monocular or binocular options of the same model, the field of view is exactly the same whether monocular or binocular.
Eye relief is a particularly important (but often overlooked) parameter for spectacle wearers if the full field of view is to be visible. Although magnification, objective lens diameter and field of view (either in degrees or m @1000m) are often shown on the body of the monocular, eye relief virtually never is (except perhaps to say "long eye relief" or "LER"). Early optics tended to have short eye relief (sub-10mm) but more contemporary designs are now much better. At least 15mm is desirable—ideally nearer 20mm—for spectacle wearers. (See table of eye reliefs below, noting the best in class, Opticron 5×30 at 25mm and Opticron 8×42 DBA at 21mm). Eye relief can seriously compromise the field of view if too short, so even if an optic has a good field of view specification, without an accompanying long eye relief, the benefit of the wide view will not be obtained (again, only applying to spectacle wearers). Good eye relief can greatly be facilitated by the eye lens diameter. The photograph below shows a comparison between two 8× monoculars, the one on the left typical of a 1980s design and with a relatively small eyepiece lens diameter (11mm) and sub-10mm eye relief. The one on the right is more contemporary—from 2016—and with a relatively large eyepiece diameter (24mm) and approximately 15mm eye relief. This large eyepiece lens not only helps eye relief but also helps to create a wider field of view. 
Two additional aspects, which are particularly relevant in the context of monoculars are:
A significant difference between binoculars and monoculars is in the focusing system. Today, binoculars almost universally use a central wheel focusing system, operating on both sides simultaneously although on some large observation binoculars, as well as some older designs, individual focusing on each eyepiece is sometimes used. Monoculars, however, employ a variety of different focusing systems, all with pros and cons. These include:
The most common is the focusing ring around the body. This retains the compactness of the unit but requires two hands to operate and does not give particularly fast focusing. In some units, the ring can be stiff to operate.
The small ring near the eyepiece also usually needs two hands to operate and in some designs can interfere with the twist-up eye cup. Being small, it can also be less convenient to operate, especially wearing gloves. The degree of twist from closest focus to infinity varies between manufacturers. Some use a very small twist (about a quarter of a turn) whereas others use a full turn or more. The small degree of twist gives a very fast focus but can be overly sensitive and in some designs too stiff to use single-handed. A full turn is a practical compromise.
A focusing wheel tends not to be used on top quality monoculars (with the exception of the Bushnell 10×42HD Legend) but is particularly popular on budget offerings from China. Although it makes the monocular more bulky, it does give very convenient focusing with one hand (via one finger) and is particularly fast and smooth, which is necessary in circumstances where quick, accurate changes of focus are important (e.g. bird watching in a wood).
A focusing lever is not common but is used, for example, on the Opticron Trailfinder. This mechanism provides very quick focusing while retaining compactness but can be stiff and overly sensitive to use and again ideally needs two hands. 
Minox and some others use a slider button, rather than a lever, on low magnification, ultra-compact designs, pushed side to side, which is also fast but rather sensitive.
Toggle focus is very rarely used (e.g. Carson Bandit 8×25). It provides a one-handed focus mechanism in a relatively large toggle, making it quick and easy to operate "in the field" with gloves but can be rather over-sensitive and difficult to fine tune.
The knurled ring around the objective lens appears to be a unique feature of the Minox 8×25 Macroscope and claims to provide quick focusing.
Some low-budget entry-level monoculars from China claim "dual focusing", which means focusing by means of twisting either the main body of the monocular, and/or the smaller ring near the eyepiece (referred to as the dioptre adjustment on binoculars). Quite why dual focusing is felt necessary on a monocular is questionable but could be for marketing reasons; there is no real technical benefit with such a system, which is never found on the top-quality monoculars from manufacturers like Opticron, Leica and Zeiss.
As with binoculars, zoom magnification is sometimes available but is virtually unknown in the best quality units (both binoculars and monoculars) as the optical quality and field of view are seriously compromised. Although zoom systems are widely and successfully used on cameras, for observation optics, zoom systems with any credibility are reserved for top quality spotting scopes and come with a very high price tag. Zoom monoculars are available from some "budget" manufacturers, which sound impressive on paper but often have extreme and unrealistic magnification ranges as well as an extremely narrow field of view.
Interpreting product specifications.
As mentioned previously, product specifications can sometimes be misleading, confusing or incorrect values stated. Such inaccuracies are more commonly found on budget items but have also sometimes been seen from some brand leaders. For those not experienced in interpreting such specifications, it is always wise to try out the item before buying wherever possible. Some of the descriptors needing particular care with include:
Specialist monoculars.
Some monoculars satisfy specialist requirements and include: 