Intensity Distribution in Single Slit Diffraction
Analysis of the variation of intensity with angle in the single-slit diffraction pattern, including the relative intensities of secondary maxima.
What is Intensity Distribution in Single Slit Diffraction?
The phenomenon of bending of light waves around obstacles or apertures and their spreading into the geometrical shadow region.
Key formula / rule: Intensity Distribution
Key points
- Describe the intensity distribution in a single-slit diffraction pattern.
- Identify the central maximum, secondary maxima, and minima.
- Apply the conditions for minima and approximate conditions for secondary maxima.
- Explain how the slit width and wavelength affect the diffraction pattern.
Common exam trap
Confusing single-slit diffraction with double-slit interference patterns.
Definitions
- Term
Diffraction
- Meaning
The phenomenon of bending of light waves around obstacles or apertures and their spreading into the geometrical shadow region.
- Term
Central Maximum
- Meaning
The brightest and widest fringe located at the center of the diffraction pattern, corresponding to θ = 0.
- Term
Secondary Maxima
- Meaning
The less intense bright fringes that appear on either side of the central maximum in a diffraction pattern.
- Term
Minima
- Meaning
The dark fringes in a diffraction pattern where the intensity of light is zero or minimum.
Learning objectives
Describe the intensity distribution in a single-slit diffraction pattern.
Identify the central maximum, secondary maxima, and minima.
Apply the conditions for minima and approximate conditions for secondary maxima.
Explain how the slit width and wavelength affect the diffraction pattern.
Use the intensity formula to qualitatively understand the pattern.
Formulae
- Name
Intensity Distribution
- Note
Where I0 is the maximum intensity at the center, and α = (πa sin θ) / λ.
- Expression
I = I0 (sin α / α)2
- Name
Condition for Minima
- Note
Where n = ±1, ±2, ±3, ... (n=0 corresponds to the central maximum).
- Expression
a sin θ = nλ
- Name
Condition for Secondary Maxima (approximate)
- Note
Where n = ±1, ±2, ±3, ...
- Expression
a sin θ = (n + 1/2)λ
- Name
Angular Width of Central Maximum
- Note
For small angles, where θ1 is the angle to the first minimum.
- Expression
2θ1 = 2λ/a
- Name
Linear Width of Central Maximum
- Note
Where D is the distance from the slit to the screen.
- Expression
W = 2Dλ/a
Prerequisites
Understanding of wave nature of light.
Concept of superposition of waves.
Basic trigonometry.
Understanding of Young's double-slit experiment (interference).
Common mistakes
Confusing single-slit diffraction with double-slit interference patterns.
Incorrectly applying the conditions for maxima and minima (e.g., using `nλ` for maxima).
Forgetting that 'n' starts from ±1 for minima and secondary maxima, not 0.
Assuming all bright fringes have equal intensity, as in double-slit interference.
Not understanding the role of the `(sin α / α)2` term in intensity variation.
Keywords
Diffraction
Single Slit
Intensity Distribution
Central Maximum
Secondary Maxima
Minima
Slit Width
Wavelength
Angular Width
Huygens' Principle
Practice preview
In a single-slit diffraction experiment, if the width of the slit is doubled, what happens to the width of the central maximum?…
easy
The intensity at the central maximum in a single-slit diffraction pattern is I₀. What is the intensity at the first secondary maximum?…
medium
If monochromatic light of wavelength λ is incident on a slit of width 'a', and the diffraction pattern is observed on a screen. Which of the following statements is INCORRECT regarding the intensity distribution?…
hard