Resolving Power of Optical Instruments: Rayleigh Criterion
Understanding the ability of an optical instrument to distinguish between two closely spaced point objects, based on Rayleigh's criterion.
What is Resolving Power of Optical Instruments: Rayleigh Criterion?
The ability of an optical instrument to produce separate images of two closely spaced point objects.
Key formula / rule: Minimum Resolvable Angular Separation (Circular Aperture)
Key points
- Define resolving power of an optical instrument.
- Explain the Rayleigh criterion for resolution.
- State the formula for the minimum resolvable angular separation for a circular aperture.
- Identify factors affecting the resolving power of optical instruments.
Common exam trap
Confusing resolving power with magnification.
Definitions
- Term
Resolving Power
- Meaning
The ability of an optical instrument to produce separate images of two closely spaced point objects.
- Term
Rayleigh Criterion
- Meaning
A condition stating that two point objects are just resolvable when the central maximum of the diffraction pattern of one object falls on the first minimum of the diffraction pattern of the other.
- Term
Angular Resolution
- Meaning
The smallest angular separation between two objects that can be distinguished by an optical instrument.
Learning objectives
Define resolving power of an optical instrument.
Explain the Rayleigh criterion for resolution.
State the formula for the minimum resolvable angular separation for a circular aperture.
Identify factors affecting the resolving power of optical instruments.
Formulae
- Name
Minimum Resolvable Angular Separation (Circular Aperture)
- Note
\θmin is the smallest angular separation between two point objects that can be distinguished. \λ is the wavelength of light, and D is the diameter of the objective aperture.
- Expression
\θmin = 1.22 \frac{\λ}{D}
- Name
Resolving Power (Angular)
- Note
Resolving power is inversely proportional to the minimum resolvable angular separation.
- Expression
R.P. = \frac{1}{\θmin}
Prerequisites
Wave nature of light
Diffraction
Interference
Properties of lenses and mirrors
Common mistakes
Confusing resolving power with magnification.
Forgetting the factor 1.22 in the Rayleigh criterion formula for circular apertures.
Assuming that increasing magnification alone improves resolution.
Keywords
Resolving Power
Rayleigh Criterion
Diffraction
Angular Resolution
Optical Instruments
Airy Disk
Minimum Resolvable Angle
Practice preview
Rayleigh's criterion is a rule of thumb for determining the resolution limit of an optical instrument. It is based on the diffraction pattern of light. For a circular aperture of diameter D, the minimum angular separatio…
hard
According to Rayleigh's criterion, two point objects are just resolved when the first minimum of the diffraction pattern of one object coincides with the maximum of the diffraction pattern of the other. What is the condi…
medium
If the wavelength of light used in a microscope is decreased by half, what happens to its resolving power, assuming other factors remain constant?…
medium