Width of Central Maximum
Calculation of the angular and linear width of the brightest central band in the single-slit diffraction pattern.
What is Width of Central Maximum?
The phenomenon where light waves spread out after passing through a narrow slit, producing an interference pattern.
Key formula / rule: Condition for Minima in Single-Slit Diffraction
Key points
- Understand the formation of the central maximum in single-slit diffraction.
- Derive the condition for the first minima.
- Calculate the angular width of the central maximum.
- Calculate the linear width of the central maximum on a screen.
Common exam trap
Confusing the position of the first minimum with the edge of the central maximum.
Definitions
- Term
Single-Slit Diffraction
- Meaning
The phenomenon where light waves spread out after passing through a narrow slit, producing an interference pattern.
- Term
Central Maximum
- Meaning
The brightest and widest bright fringe in the single-slit diffraction pattern, located at the center.
- Term
Minima
- Meaning
Points or regions in a diffraction or interference pattern where the intensity of light is zero or very close to zero.
Learning objectives
Understand the formation of the central maximum in single-slit diffraction.
Derive the condition for the first minima.
Calculate the angular width of the central maximum.
Calculate the linear width of the central maximum on a screen.
Analyze the dependence of the central maximum's width on slit width and wavelength.
Formulae
- Name
Condition for Minima in Single-Slit Diffraction
- Note
where 'a' is slit width, θ is the angle of diffraction, 'n' is the order of the minimum (n = 1, 2, 3,...).
- Expression
a sin θ = nλ
- Name
Angular Width of Central Maximum
- Note
where θ is the angle for the first minimum (n=1).
- Expression
2θ
- Name
Linear Width of Central Maximum on Screen
- Note
Valid for D >> a, where 'D' is the distance from the slit to the screen and 'λ' is the wavelength of light.
- Expression
w ≈ 2λD/a
Prerequisites
Wave nature of light
Interference
Huygens' Principle
Concept of minima and maxima in diffraction patterns
Trigonometry (sine, tangent, small angle approximation)
Common mistakes
Confusing the position of the first minimum with the edge of the central maximum.
Forgetting the factor of 2 when calculating the total width (angular or linear).
Using the formula for minima positions (a sin θ = nλ) incorrectly for the central maximum's boundaries (which are the first minima, n=1).
Assuming small angle approximation when it's not valid.
Keywords
Single-slit diffraction
Central maximum
Diffraction pattern
Minima
Wavelength
Slit width
Angular width
Linear width
Diffraction angle
Practice preview
In a single-slit diffraction experiment, the width of the central maximum is directly proportional to:…
easy
In a single-slit diffraction experiment, if the slit width is increased by a factor of 4, while keeping the wavelength and screen distance constant, the width of the central maximum will:…
medium
If the wavelength of light used in a single-slit diffraction experiment is doubled, the width of the central maximum will:…
easy