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The resolving power of a microscope is the inverse of the distance between the objects that are just resolved. The resolving power of a microscope depends upon the wavelength of light, refractive index, and angular aperture.

The argon ion laser can be operated as a continuous gas laser at about 25 different wavelengths in the visible between 408.9 and 686.1nm, but is best known for its most efficient transitions in the green at 488 nm and 514.5 nm. Operating at much higher powers than the helium-neon gas laser, it is not uncommon to achieve 30 to 100 watts of continuous power using several transitions. This output is produced in a hot plasma and takes extremely high power, typically 9 to 12 kW, so these are large and expensive devices.

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The resolving power of a telescope can be defined as the inverse of the smallest angle subtended at the lens aperture by two point objects at a far away distance from the point of observation which can be distinguished to be “just separate” in that focal plane.

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For a microscope, we follow Abbe’s criterion and can obtain the mathematical expression as = \(\dfrac {2nsin\theta}{\lambda}\)

The inverse of the square of distances or the length of separation between two points or objects that can be just resolved when viewed through an optical instrument is known as the resolving power of that instrument. The resolving power of human eye is considered to be about one arc minute or 60 arc seconds.

There is no generalized formula for resolving power of an optical instrument. It depends from one instrument to another.

In this article, you will learn in detail about the concept of resolving power, its formula, values and various applications.

The carbon dioxide gas laser is capable of continuous output powers above 10 kilowatts. It is also capable of extremely high power pulse operation. It exhibits laser action at several infrared frequencies but none in the visible. Operating in a manner similar to the helium-neon laser, it employs an electric discharge for pumping, using a percentage of nitrogen gas as a pumping gas.

Gas laserdiagram

Large apertures are required to resolve the power of a telescope and cosmic objects. For example, a system of binary stars subtends a small angle on the telescope.

The helium gas in the laser tube provides the pumping medium to attain the necessary population inversion for laser action.

Helium-neon lasers are common in the introductory physics laboratories, but they can still be dangerous! According to Garmire, an unfocused 1-mW HeNe laser has a brightness equal to sunshine on a clear day (0.1 watt/cm2) and is just as dangerous to stare at directly.

Gas laserexample

Resolving power is the ability of an instrument to separate two adjacent points from each other from a considerable distance. Louis de Broglie put forward the concept of resolving power from the phenomenon of wave nature of electrons from the de Broglie hypothesis.

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The resolving power of an electron microscope is 10 angstrom whereas the resolving power of a compound microscope is 0.25μm. The resolving power is the same for a light microscope too.

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This shows the beams from two helium-neon lasers passing through two lenses arranged in the Galilean telescope geometry. The beams were made visible with a spray can of artificial smoke.

NASA’s James Webb telescope is the largest telescope built till now for studying infrared radiation of the interstellar and beyond.

The most common and inexpensive gas laser, the helium-neon laser is usually constructed to operate in the red at 632.8 nm. It can also be constructed to produce laser action in the green at 543.5 nm and in the infrared at 1523 nm.

Resolving power is an observed measure; it does not have any S.I unit because it is a mathematical ratio between mean wavelengths.

One of the excited levels of helium at 20.61 eV is very close to a level in neon at 20.66 eV, so close in fact that upon collision of a helium and a neon atom, the energy can be transferred from the helium to the neon atom.

Where n is the refractive index of the medium for a better resolution. The value of \(nsin\theta\) must be high, which in practice means, the object lens of the microscope is to be kept as close to the object of observation and to use a medium which generally has a higher refractive index.

Rayleigh’s criterion is one of the most important principles in understanding the resolution of an instrument. It states that two images are just resolvable when the centre of the diffraction pattern is directly over the first minimum diffraction pattern of the other. This law determines the diffraction limit to resolution for a particular instrument. This can be understood from the diagram below.

The CO2 laser is the most efficient laser, capable of operating at more than 30% efficiency. That's a lot more efficient than an ordinary incandescent light bulb at producing visible light (about 90% of the output of a lightbulb filament is invisible).