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Wave Optics & Wave Diffraction

Diffraction of Light

Explore how light bends around obstacles and spreads through narrow openings. Adjust slit widths and wavelengths to watch the central maximum expand, examining intensity graphs and the single-slit equation.

Single Slit Diffraction Lab ⓘ

Observe single slit diffraction patterns, intensity graphs, and wave propagation.

Simulation active

Diffraction Telemetry

a sinθ = λ
Wavelength (λ)
600 nm
Slit Width (a)
0.10 mm
Screen Distance (D)
2.00 m
Diffraction Angle (θ)
0.34°
Central Max Width
24.00 mm

Postulates of Single Slit Diffraction

When light passes through a narrow aperture of size a comparable to its wavelength λ, it spreads outwards instead of traveling in straight geometric rays. This spreading produces a central maximum band flanked by weaker, alternating dark and bright bands, called single-slit diffraction:

  • Inverse Slit Width Scaling: The diffraction angle θ is inversely proportional to the slit width a. Narrowing the slit causes the light to bend at sharper angles, widening the diffraction pattern.
  • Minima Condition: Minima (dark bands) are formed when the path difference between wavelets from opposite edges of the slit is a multiple of wavelength: a sinθ = mλ.

What is Diffraction?

Diffraction is the bending of light waves around obstacles or as they pass through narrow slits, allowing light to propagate into regions of geometrical shadow.

Thomas Young's double-slit experiment uses diffraction at each individual slit to create two overlapping, coherent wavefronts.

Single Slit Minima Formula

The positions of dark fringes (minima) are given by the equation:

Diffraction Minima Condition

a × sinθ = m × λ

Here, a is the slit width, θ is the angle, λ is the wavelength, and m is the integer order (m = ±1, ±2, ...).

Central Maximum Width

The central bright band is twice as wide as any secondary maximum fringe. Its linear width on a screen at distance D is:

W = 2 × λ × D / a

Narrower slits (smaller a) or longer wavelengths (larger λ) make the central maximum significantly wider.

Step-by-Step Solved Problems

Practice using the diffraction formulas with these step-by-step mathematical examples.

Example 1 Problem Statement

A laser light of wavelength 600 nm passes through a single slit of width 0.12 mm. The diffraction pattern is observed on a screen placed 2.0 m away. Calculate the width of the central maximum.

View Mathematical Solution Steps
  1. Identify given values: Wavelength λ = 600 nm = 6 × 10-7 m, Slit width a = 0.12 mm = 1.2 × 10-4 m, Screen distance D = 2.0 m.
  2. Recall the formula for the linear width of the central maximum: W = 2λD / a.
  3. Substitute values: W = (2 × 6 × 10-7 m × 2.0 m) / (1.2 × 10-4 m).
  4. Calculate: W = (2.4 × 10-6) / (1.2 × 10-4) = 0.02 m = 20 mm.

Final Derived Answer: Width of the central maximum W = 20.0 mm.

Example 2 Problem Statement

In a single-slit diffraction experiment, the first minimum is formed at an angle of 30° for light of a certain wavelength. If the slit width is 1.2 micrometers, find the wavelength of the light.

View Mathematical Solution Steps
  1. Identify given values: Diffraction angle θ = 30°, Slit width a = 1.2 μm = 1.2 × 10-6 m, Minima order m = 1.
  2. Recall the condition for single-slit minima: a sinθ = mλ.
  3. Solve for wavelength: λ = a sinθ / m.
  4. Substitute values: λ = (1.2 × 10-6 m × sin 30°) / 1.
  5. Calculate: λ = 1.2 × 10-6 × 0.5 = 6.0 × 10-7 m = 600 nm.

Final Derived Answer: Wavelength λ = 600 nm.

Example 3 Problem Statement

A single-slit diffraction setup is illuminated by light of 500 nm. If the width of the central maximum on a screen 1.5 m away is 15 mm, find the slit width.

View Mathematical Solution Steps
  1. Identify given values: Wavelength λ = 500 nm = 5 × 10-7 m, Screen distance D = 1.5 m, Central max width W = 15 mm = 1.5 × 10-2 m.
  2. Recall the linear width formula: W = 2λD / a.
  3. Rearrange for slit width a: a = 2λD / W.
  4. Substitute values: a = (2 × 5 × 10-7 m × 1.5 m) / (1.5 × 10-2 m).
  5. Calculate: a = (1.5 × 10-6) / (1.5 × 10-2) = 1.0 × 10-4 m = 0.10 mm.

Final Derived Answer: Slit Width a = 0.10 mm.

Self-Check Questions

Question 1

Define the diffraction of light and state the physical condition necessary for it to occur.

Show Answer & Explanation

Diffraction is the bending of light waves around the edges of an obstacle or slit, spreading into the geometrical shadow zone. For diffraction to be noticeable, the physical size of the opening or obstacle (a) must be of the same order of magnitude as, or smaller than, the wavelength of the light (λ).

Question 2

Why does a single-slit diffraction pattern have a very bright center while the secondary maxima fade rapidly?

Show Answer & Explanation

The central maximum occurs at θ = 0, where wavelets from all parts of the slit arrive at the screen in phase, interfering constructively. Secondary maxima occur because wavelets from different parts of the slit only partially cancel each other out, leaving a small fraction of light energy to form weaker side bands.

Question 3

Contrast the single-slit diffraction pattern with the double-slit interference pattern.

Show Answer & Explanation

In double-slit interference, all bright fringes have nearly equal brightness and width. In single-slit diffraction, the central bright maximum is twice as wide as the secondary maxima, and the brightness of the side maxima decreases rapidly as we move away from the center.

Question 4

How does narrowing the slit width affect the width and brightness of the central maximum?

Show Answer & Explanation

Narrowing the slit width "a" increases the angular spread of the central maximum (θ ≈ λ/a), causing it to become wider. However, because less light passes through a smaller opening and spreads over a larger area, the brightness of the central maximum decreases.

Question 5

What happens to the diffraction pattern on a screen if the monochromatic laser is replaced by a white light source?

Show Answer & Explanation

The central maximum will appear white in the middle. The secondary maximum bands will appear colored, with violet on the inside (closest to center, shorter λ) and red on the outside (further away, longer λ), because each color diffracts at a different angle.

Question 6

State the mathematical formula for the angular positions of the minima (dark fringes) in single-slit diffraction.

Show Answer & Explanation

The condition for minima is: a sinθ = mλ, where "a" is the slit width, θ is the diffraction angle, λ is the wavelength of light, and m is a non-zero integer (m = ±1, ±2, ±3, ...).