RESOLVING POWER OF OPTICAL INSTRUMENTS

Concept of Resolving Power: When light from a point-source passes through an optical instrument, the image of the point-objects is not a sharp point, but a spot is obtained which is called the diffraction pattern. This happens because of the wave-form of light. Hence if two point objects are very close to each other, then their diffraction patterns will also be very close and will overlap each other. If the overlapping in the diffraction patterns is small, then both the objects are seen separate in the optical instrument i.e, the optical instrument is able to resolve the objects. If, however, the overlapping is large, then the objects will not be seen as separate; they will be seen as one. In other words the optical instrument is not resolving them. The power of an optical instrument to produce distinctly separate images of two close objects is called the ‘resolving power’ of that instrument.

One eye is also an optical instrument. If two small objects are placed very close to each other, then it is not necessary that our eye see them separate. This can be seen by a simple experiment. Suppose there is a wall before us on which is pasted a white paper having a number of back parallel lines drawn at separations of 2 mm. When we are quite near the wall, these lines are seen as separate. But as we move away from the wall, a stage is reached when the lines appear mixing with each other and we can no longer distinguish that the lines are separated from one another.

As we move away from the wall, the angle subtended at our eye by any two lines goes on decreasing. From this we conclude that seeing two close objects as separate depends upon the angle subtended by them at the eye. It is seen by experiment that if this angle is less than 1¢ (1 minute) or 1

60

F

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°

then lines will not be seen as separate. This angle is called the ‘resolving limit’ of the eye.

Similarly, an optical instrument has a limit to form separate images of two objects placed very close to each other. That minimum distance between two objects when they can be seen as separate by an optical instrument is called the ‘limit of resolution’ of that instrument. Smaller the limit of resolution of an optical instrument, greater is said to be its resolving power.

Resolving Power of Telescope : Necessity of Large-aperture Objective: The resolving power of a telescope is its ability to show two distant closely-lying objects as just separate. The reciprocal of resolving power is the limit of resolution¢ of the telescope.

The limit of resolution of telescope is measured by the angle subtended at its objective by those two distant objects which are seen just separate through the telescope. Its value is directly proportional to the wavelength l of the light used and inversely proportional to the aperture (diameter) d of the objective of the telescope.

Limit of resolution of telescope µ l

d = 1 22.

l

d radian.

Telescope is used to see distant objects which are generally seen in sunlight. Therefore, we have no control on l. Hence, to reduce the limit of resolution of a telescope., we must use objective lens of large aperture (d). Larger the aperture of the objective lens, smaller the limit of resolution, or greater the resolving power of the telescope.

There is also an additional advantage of large objective. It sends greater amount of light in the telescope and so intense images are formed. Thus, objects extremely far away (whose luminosity ap- pears feeble because of distance) can also be seen.

Resolving Power of Microscope : Necessity of Light of Small Wavelength: The resolving power of a microscope is its ability to show two nearly closely-lying objects as just separate. The reciprocal of resolving power is the ‘limit of resolution’ of the microscope.

The limit of resolution of microscope is measured by the mini- mum distance between those two point-objects which are seen just separate through the microscope. Its value is directly proportional to the wavelength l of light and inversely proportional to the angle of the cone of lights-rays from any one object entering the microscope:

Limit of resolution of microscope µ l

cone angle

If the angle of the cone of light rays entering the objective of a microscope be 2a (Fig. 2.22), then

Limit of resolution of microscope µ l

a 2 = 1 22. . l a 2 sin

If instead of air a liquid of refractive index n be filled between the object and the objective

of the microscope, then the limit of resolution will become 1 22

2 . . l a nsin

Microscope is used to see close objects (such as biological slides, minute particles etc). Those objects are illuminated by a light source. Now, to reduce the limit of resolution of a microscope, we cannot increase the cone-angle (because then the aperture of the lens will have to be increased), but we can decrease l. For example, we can reduce the limit of resolution by using blue light instead of ordinary light. In visible light the minimum wavelength is 4000 Å. If the distance between two objects is less than this, then we cannot see them separate in the visible light by means of a microscope.