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Single-Slit Diffraction Condition Calculator

This equation determines the angular positions of dark fringes (minima) in a single-slit diffraction pattern.

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Angle

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Overview

When monochromatic light passes through a narrow slit of width 'a', it undergoes diffraction, creating an interference pattern on a distant screen. The condition a*sin(theta) = +/- n*lambda identifies the angles at which destructive interference occurs, resulting in dark fringes. This phenomenon demonstrates the wave nature of light and is limited by the slit width relative to the wavelength.

Symbols

Variables

a = Slit Width, = Angle, n = Fringe Order, = Wavelength

Slit Width
Angle
rad
Fringe Order
dimensionless
Wavelength

Apply it well

When To Use

When to use: Use this equation when calculating the angular position of dark fringes in a single-slit diffraction experiment where the slit width is known.

Why it matters: It explains the fundamental limits of optical resolution in instruments like telescopes and microscopes, where diffraction sets a limit on how close two objects can be while still being distinguished.

Avoid these traps

Common Mistakes

  • Confusing the single-slit dark fringe condition with the double-slit bright fringe condition.
  • Forgetting that n cannot be zero, as n=0 corresponds to the central maximum.
  • Using degrees instead of radians when performing calculations if the calculator mode is set incorrectly.

One free problem

Practice Problem

A laser with a wavelength of 633 nm passes through a slit of width 0.05 mm. Calculate the angle (in radians) of the first dark fringe (n=1).

Slit Width0.00005 m
Fringe Order1 dimensionless
Wavelength6.33e-7 m

Solve for: theta

Hint: Use the formula sin(theta) = (n * lambda) / a. For small angles, sin(theta) is approximately theta.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of Physics (10th ed.). Wiley.
  2. Young, H. D., & Freedman, R. A. (2020). University Physics with Modern Physics (15th ed.). Pearson.
  3. University Physics Textbook (e.g., Serway & Jewett, Giancoli)
  4. NIST CODATA
  5. IUPAC Gold Book
  6. Wikipedia: Single-slit diffraction
  7. Halliday, Resnick, and Walker: Fundamentals of Physics
  8. Hecht: Optics