Diffraction
Single slit diffraction pattern, width of the central maximum and resolving power. (Physics › Wave Optics, NEET UG syllabus.)
What is Diffraction?
The phenomenon of bending of light waves around obstacles or apertures, causing them to spread into regions of geometrical shadow.
Key formula / rule: Condition for minima in single-slit diffraction
Key points
- Define diffraction and explain its causes.
- Describe the single-slit diffraction pattern.
- Derive and apply the condition for minima in single-slit diffraction.
- Calculate the angular and linear width of the central maximum.
Common exam trap
Confusing diffraction with interference (though they are related, diffraction is the interference of secondary wavelets from a single wavefront).
Definitions
- Term
Diffraction
- Meaning
The phenomenon of bending of light waves around obstacles or apertures, causing them to spread into regions of geometrical shadow.
- Term
Fraunhofer Diffraction
- Meaning
A type of diffraction where both the source and the screen are effectively at infinite distances from the diffracting aperture/obstacle, resulting in parallel rays.
- Term
Rayleigh Criterion
- Meaning
States that two adjacent point objects are just resolved when the center of the diffraction pattern of one coincides with the first minimum of the diffraction pattern of the other.
- Term
Resolving Power
- Meaning
The ability of an optical instrument to distinguish between two closely spaced objects or their images as separate entities.
- Term
Numerical Aperture (NA)
- Meaning
A measure of the ability of an objective lens to gather light and resolve fine specimen detail, defined as `n sin β`, where 'n' is the refractive index of the medium between the object and the objective, and 'β' is half the angular aperture.
Learning objectives
Define diffraction and explain its causes.
Describe the single-slit diffraction pattern.
Derive and apply the condition for minima in single-slit diffraction.
Calculate the angular and linear width of the central maximum.
Define resolving power and state Rayleigh's criterion.
Apply formulae for resolving power of telescopes and microscopes.
Explain how diffraction limits the resolution of optical instruments.
Formulae
- Name
Condition for minima in single-slit diffraction
- Note
Where 'a' is slit width, 'θ' is diffraction angle, 'λ' is wavelength, 'n' = ±1, ±2, ±3, ...
- Expression
a sin θ = nλ
- Name
Angular width of central maximum
- Note
For small angles, where 'a' is slit width, 'λ' is wavelength.
- Expression
Δθ ≈ 2λ/a
- Name
Linear width of central maximum
- Note
Where 'D' is distance to screen, 'a' is slit width, 'λ' is wavelength.
- Expression
W = 2Dλ/a
- Name
Angular resolution of a telescope
- Note
Where 'λ' is wavelength, 'D' is diameter of objective lens.
- Expression
θmin = 1.22λ/D
- Name
Resolving power of a telescope
- Note
Inverse of angular resolution.
- Expression
RP = D/(1.22λ)
- Name
Minimum resolvable distance for a microscope
- Note
Where 'λ' is wavelength, 'n sin β' is numerical aperture.
- Expression
dmin = 1.22λ / (2n sin β)
- Name
Resolving power of a microscope
- Note
Inverse of minimum resolvable distance.
- Expression
RP = (2n sin β) / (1.22λ)
Prerequisites
Understanding of wave nature of light.
Huygens' Principle.
Concept of interference of light waves.
Basic trigonometry and small angle approximations.
Common mistakes
Confusing diffraction with interference (though they are related, diffraction is the interference of secondary wavelets from a single wavefront).
Using `n` for maxima in diffraction as in Young's Double Slit Experiment (in single-slit, `n` refers to minima).
Incorrectly applying the small angle approximation (`sin θ ≈ θ`) when not appropriate.
Forgetting the factor `1.22` in Rayleigh's criterion formulae.
Not understanding that higher resolving power means smaller `θmin` or `dmin`.
Keywords
Diffraction
Single Slit
Central Maximum
Minima
Angular Width
Linear Width
Resolving Power
Rayleigh Criterion
Telescope
Microscope
Numerical Aperture
Wavelength
Slit Width
Practice preview
A telescope has an objective lens of diameter 20 cm. If it is used to observe light of wavelength 6000 Angstrom, what is its resolving power?…
hard
What phenomenon describes the bending of light waves around obstacles or through small apertures?…
easy
For diffraction to be significant and easily observable, the size of the aperture or obstacle should be comparable to which of the following?…
easy