Diffraction at a Single Slit
Detailed study of the diffraction pattern produced when monochromatic light passes through a single narrow slit.
What is Diffraction at a Single Slit?
The phenomenon of bending and spreading of light waves when they pass through a narrow aperture or around an obstacle.
Key formula / rule: Condition for Minima
Key points
- Understand the phenomenon of diffraction at a single slit.
- Describe the characteristics of the single-slit diffraction pattern.
- Derive and apply the conditions for minima and secondary maxima.
- Relate the width of the slit and the wavelength of light to the diffraction pattern.
Common exam trap
Confusing the conditions for minima and maxima.
Definitions
- Term
Diffraction
- Meaning
The phenomenon of bending and spreading of light waves when they pass through a narrow aperture or around an obstacle.
- Term
Single Slit
- Meaning
A narrow rectangular opening used to observe diffraction patterns.
- Term
Principal Maximum
- Meaning
The central bright band in a diffraction pattern, which is the most intense and widest.
- Term
Minima
- Meaning
Dark bands in the diffraction pattern where the intensity of light is zero (ideally).
- Term
Secondary Maxima
- Meaning
Fainter bright bands located between the minima in a diffraction pattern.
Learning objectives
Understand the phenomenon of diffraction at a single slit.
Describe the characteristics of the single-slit diffraction pattern.
Derive and apply the conditions for minima and secondary maxima.
Relate the width of the slit and the wavelength of light to the diffraction pattern.
Formulae
- Name
Condition for Minima
- Note
where 'a' is the slit width, 'θ' is the angle from the center, 'n' is an integer (±1, ±2, ±3, ...), and 'λ' is the wavelength of light. n=0 corresponds to the central maximum.
- Expression
a sin θ = nλ
- Name
Condition for Secondary Maxima
- Note
where 'n' is an integer (±1, ±2, ±3, ...). These are approximate positions as the intensity decreases rapidly.
- Expression
a sin θ ≈ (n + 1/2)λ
- Name
Angular Width of Central Maximum
- Note
This is the angle between the first minima on either side of the central maximum.
- Expression
Δθ ≈ 2λ/a
- Name
Linear Width of Central Maximum on Screen
- Note
where 'f' is the distance of the screen from the slit (or focal length of a lens placed after the slit).
- Expression
Δx ≈ 2fλ/a
Prerequisites
Wave nature of light
Huygens' principle
Concept of interference
Basic trigonometry
Common mistakes
Confusing the conditions for minima and maxima.
Assuming that the diffraction pattern is a sharp image of the slit.
Not considering the decrease in intensity of secondary maxima.
Incorrectly applying the formula for interference instead of diffraction.
Keywords
Diffraction
Single Slit
Wave Optics
Huygens' Principle
Diffraction Pattern
Minima
Maxima
Wavelength
Slit Width
Practice preview
In single-slit diffraction, the intensity of the secondary maxima decreases rapidly because:…
medium
When monochromatic light is diffracted by a single slit, the intensity of the diffracted light at different points on the screen is described by:…
easy
In the diffraction pattern of a single slit, the width of the central maximum is determined by the:…
easy