Question
Discuss Rayleigh’s criterion for resolving power of an optical instrument. Obtain an expression for resolving power of a microscope.
Answer :
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The resolving power of an optical instrument refers to its ability to distinguish between two closely spaced points or objects. When two point sources are very close to each other, the images formed by the optical instrument may overlap, making it difficult to distinguish them. Lord Rayleigh formulated a criterion, known as Rayleigh’s criterion, which provides a practical limit for resolution based on the diffraction of light. According to Rayleigh’s criterion, two point sources are just resolvable when the principal maximum of the diffraction pattern of one source coincides with the first minimum of the diffraction pattern of the other. This criterion essentially defines the smallest angular separation between two points at which they can still be distinguished as separate. Mathematically, if a circular aperture is used, the diffraction pattern produced by a point source is an Airy disk, with the radius of the first dark ring given by ( \theta = 1.22 \frac{\lambda}{D} ), where ( \lambda ) is the wavelength of light used and ( D ) is the diameter of the aperture. According to Rayleigh’s criterion, the minimum angular separation ( \theta_\text{min} ) for just-resolvable objects is therefore (
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