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Understanding Physics Topics is essential for solving complex problems in many fields, including engineering and medicine.
What is Resolving Power of Microscope and Astronomical Telescope?
Two types of resolving power are relevant for different optical instruments:
- Spatial resolving power and
- Spectral resolving power.
Spatial or angular resolving power: Our eye is an optical instrument. If two point objects (or their images) are very close to each other our eyes may not see them as separate objects. They seem to be the same object or same image. It can be verified by a simple experiment.
Let a white paper be fixed on a wall in front of us. On the paper some black parallel lines are drawn at 2 mm distance apart. When we stand very close to the wall, we can see all the parallel lines. When we gradually move away from the wall, the angle formed by any two lines at our eye gets diminished and at one point it seems that the lines have merged with each other i.e., the lines can no longer be identified separately.
It can be inferred that whether two objects placed side by side can be differentiated, depends on the angle formed by the two objects at our eyes. It has been established through experiments that, if the angle becomes less than 1 minute or \(\frac{1}{60}\) degree, eyes will not be able to see two objects separately. This angle is called the angular limit of resolution of our eyes. This means our eyes as well as an optical instrument has its own limit of resolving images of two different objects located very near to each other.
Limit of Resolution: The smallest linear distance or the angular separation between two objects which can be just distinctly seen through an optical instrument, is called the spatial limit of resolution of that instrument.
Resolving power: The power or ability of an optical instrument to produce distinctly separate images of two close objects, is called the spatial resolving power of the instrument.
Spatial resolving power is measured by the reciprocal of the limit of resolution. If Δx or Δθ be the linear or angular limit, then the resolving power would be \(\frac{1}{\Delta x}\) or \(\frac{1}{\Delta \theta}\) respectively.
Spectral resolving power: Instruments like prism and diffraction grating are used to separate spectral lines of different wavelengths. For example, the D1 and D2 lines of sodium spectrum have a separation of 6 Å of wavelength between them.
Usually, a prism cannot separate them, but a diffraction grating can. So we say that the limit of resolution of a grating is 6 Å or less, wheras that of a prism is greater than 6 Å.
If an optical instrument just resolves two spectral lines of wavelengths λ and λ + Δλ, then its limit of resolution is defined as Δλ, and its spectral resolving power as \(\frac{\lambda}{\Delta \lambda}\).
Rayleigh criterion: This defines the spectral limit of resolution of an optical instrument. Its statement is:
Two images are said to be just resolved when the central maximum in the diffraction pattern due to one of them is situated at the first minimum in the diffraction pattern due to the other.
It is to be noted that, spatial resolving power is intimately related to spectral resolving power; because, to observe the spatial separation between two objects, we often have to use instruments working on the principle of wavelength separation, phenomenon of diffraction, etc.
Resolving power of Microscope
If a microscope is able to show the images of two point objects, lying close to each other, separately, then the reciprocal of the distance between these two objects is the resolving power of that microscope.
This power depends on the wavelength (λ) of light used, refractive index (µ) of the medium between two objects and the objective of the microscope and cone angle (θ) formed by the radius of the objective on any one of the object.
If the internal distance between two objects be Δd, then resolving power of the microscope
R = \(\frac{1}{\Delta d}\) = \(\frac{2 \mu \sin \theta}{\lambda}\)
To increase the resolving power of a microscope, the objects and the objective of the instrument are immersed in oil. Hence, as the value of μ increases, the resolving power, R also increases.
The expression μ sin θ is called the numerical aperture of a microscope. it is a special characteristic of a microscope. It is mentioned in some microscopes.
Resolving power of Astronomical Telescope
When a telescope is able to analyse distinctly two separate distant objects lying closely, then the reciprocal of the angle subtended by the two objects at its objective is called the resolving power of that telescope.
If the angle subtended, by the two objects at objective, be Δθ, then resolving power of the telescope,
R = \(\frac{1}{\Delta \theta}\) = \(\frac{a}{1.22 \lambda}\)
[where a = diameter of the objective of the telescope]
Hence, if the diameter of the objective of the telescope is increased, its resolving power increases. Again if the wavelength of the incident light decreases, the resolving power increases.
1. The angular spread Δθ of a telescope depends solely on its objective. If objective of a telescope is unable to analyse two stars located extremely far away, then these stars cannot be analysed by the telescope even by increasing the magnification of its eye piece.
2. To see different astronomical objects In the sky, telescopes with objective having diameter 1 mm or more are used.