WAV-08

Young double-slit fringe

Δy = λ L / d between adjacent bright fringes.

Reading speed

InterferenceYoung 1801

Governing equation

\Delta y=\dfrac{\lambda L}{d}

$d \in \left[0.02, 4\right]$

where

\lambda: Wavelength (nm)
L: Screen distance (m)
d: Slit spacing (mm)
\Delta y: Fringe spacing (mm)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

00:0 / 00:08

①

Governing law — red

\Delta y=\dfrac{\lambda L}{d}

$d \in \left[0.02, 4\right]$

$d = 0.02$ $\Delta y = 31.92$

Along the curve

②

Domain of the variable — blue

d_{\min} = 0.02,\quad d_{\max} = 4

$d \in \left[0.02, 4\right]$

$d = 0.02$ $d = 0.02$

Along the curve

③

Response curve — green

\Delta y=\dfrac{\lambda L}{d}

$d \in \left[0.02, 4\right]$

$d = 0.02$ $\Delta y = 31.92$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\Delta y}{\mathrm{d}d}

$d \in \left[0.02, 4\right]$

$d = 0.045$ $\Delta y^{\prime} = -455.6$

Along the curve

Lecture brief

Historical brief

d’Alembert’s wave equation, Snell, the thin-lens maker, Doppler and Bragg interference are the classical optics-and-sound toolkit. The lab is propagation, image and shift. This sheet (WAV-08 — Young double-slit fringe) is the form associated with Young 1801. Working symbols: $\lambda$ , $L$ , $d$ $\rightarrow$ $\Delta y$ . Two coherent slits a distance d apart produce a path difference d sin θ; small-angle bright fringes sit at y = n λ L / d.

Purpose

Purpose: compute

\Delta y

from

\lambda

L

d

in Waves & optics via

\Delta y=\dfrac{\lambda L}{d}

Δy = λ L / d between adjacent bright fringes. Use it when a real waves & optics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\lambda = 532.000\,\mathrm{nm}

L = 1.200\,\mathrm{m}

d = 0.250\,\mathrm{mm}

, the governing relation

\Delta y=\dfrac{\lambda L}{d}

yields

\Delta y = 2.5536\,\mathrm{mm}

. Fraunhofer, small angle, equal slits. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Wavelength \lambda532 nmScreen distance L1.2 mSlit spacing d0.25 mm

Outputs

Fringe spacing \Delta y2.5536 mm

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Fraunhofer, small angle, equal slits.

Two coherent slits a distance d apart produce a path difference d sin θ; small-angle bright fringes sit at y = n λ L / d.

Reading speed

Watch on YouTube