Diffraction Calculator
Free online single and double slit diffraction calculator using Fraunhofer wave optics formulas. Compute fringe positions in mm, diffraction angles, and central maximum angular width for physics labs and classroom demonstrations.
About This Calculator
This diffraction calculator uses Fraunhofer (far-field) wave optics to compute the positions and angles of interference fringes for both single slit and double slit configurations. Enter the light wavelength, slit dimensions, screen distance, and maximum order to generate a complete diffraction pattern with angular and linear positions.
Physics Formulas Used
Single Slit Minima: a · sin(theta) = mlambda, where a is the slit width, theta is the diffraction angle, m is the order (m = +/-1, +/-2, ...), and lambda is the wavelength.
Double Slit Maxima: d · sin(theta) = mlambda, where d is the slit separation. The fringe position on the screen is y = L · tan(theta), where L is the screen distance.
Central Angular Width (Single Slit): Deltatheta = 2lambda / a (radians), measuring the angular span between the first minima on either side.
Applications
Diffraction analysis is essential in spectroscopy (determining wavelengths), optical instrument design (resolution limits), X-ray crystallography (Bragg diffraction), and classroom physics demonstrations. This calculator supports the standard wave optics curriculum across IIT JEE (India), AP Physics (US), and A-Level Physics (UK) examinations.
Regional Context
India (IIT JEE / NEET): Problems typically use sodium light (589 nm) with slit widths of 0.1-1 mm. Understanding the sinc^2 intensity envelope and central maximum broadening is critical for JEE Advanced wave optics questions.
United States (AP Physics 2): Lab experiments use red laser diodes (650-670 nm) with variable slit sets. Students measure fringe spacing and verify the inverse relationship between slit width and fringe spread.
United Kingdom (A-Level Physics): The AQA and Edexcel specifications cover Fraunhofer diffraction at a single slit and Young's double slit experiment. Students use 589 nm sodium vapour lamps and diffraction gratings to measure wavelengths.
Frequently Asked Questions
What is the difference between single slit and double slit diffraction?
In single slit diffraction, light passing through one narrow slit spreads and forms a central bright fringe with dimmer fringes on either side, caused by interference of waves from different parts of the same slit. In double slit (Young's) diffraction, light from two narrow slits interferes to produce sharp equally spaced bright and dark fringes. The single slit formula a·sin(theta) = mlambda gives minima positions, while the double slit formula d·sin(theta) = mlambda gives maxima positions.
How do I calculate the position of diffraction fringes on the screen?
First compute the diffraction angle theta using sin(theta) = mlambda / a (single slit minima) or sin(theta) = mlambda / d (double slit maxima), where lambda is wavelength, a is slit width, d is slit separation, and m is the order number. Then find the linear position y = L·tan(theta) where L is the screen distance from the slit. The calculator does this automatically for all visible orders up to your specified maximum.
What is the central maximum angular width in single slit diffraction?
The central maximum angular width is given by 2lambda / a (in radians), where lambda is the wavelength and a is the slit width. This represents the angular span between the first minima on either side of the central bright fringe. The width increases with longer wavelengths and narrower slits, which is why red light diffracts more than blue light through the same slit.
What are typical wavelength values used in diffraction experiments?
Common laboratory wavelengths include: sodium D-line at 589 nm (yellow), helium-neon laser at 632.8 nm (red), and argon laser at 488 nm (blue). In Indian IIT JEE and NEET problems, 500 nm to 600 nm visible light is standard. US AP Physics labs often use 650 nm red laser diodes. UK A-Level physics courses use 589 nm sodium light or 633 nm He-Ne lasers for diffraction experiments.
Why do higher order fringes become fainter?
Higher order fringes become fainter due to the sinc^2 intensity envelope of single slit diffraction. Even in double slit experiments, each slit has a finite width that modulates the interference pattern. The intensity of maxima decreases approximately as 1/m^2, where m is the order number. In practice, orders beyond m=3 or m=4 are often too dim to observe without sensitive detectors.
What happens if sin(theta) exceeds 1 for a given order?
When mlambda / a or mlambda / d exceeds 1, that order does not exist physically because the required angle of diffraction would exceed 90 degrees. The calculator automatically skips these invisible orders. The total number of visible orders is limited by the ratio of slit dimension to wavelength. For example, with 500 nm light and a 100 mum slit, the highest visible minimum is around m = 200.
How do I set up a Young's double slit experiment?
Shine a coherent light source (laser or filtered monochromatic light) at two narrow parallel slits typically 0.1-0.5 mm apart, placed 0.5-2 m from a viewing screen. The interference pattern appears as alternating bright and dark fringes. Measure fringe spacing Deltay = lambdaL / d and compare with calculated values. Use slit separations of 200-500 mum and screen distances of 1 m for optimal classroom results.