01 / THE OPTICAL BENCH
SCHEMATIC SCALEThe screen, waves and all numerical controls below remain available.
02 / SCREEN & DETECTOR
TIME AVERAGE03 / WAVES AT P
Equal optical paths give a bright centre. Insert glass into arm 1 to delay its arriving wave.
The model, equations & limits
From path to phase to intensity
r₁ = √[L² + (y − d/2)²]
r₂ = √[L² + (y + d/2)²]
Δ = r₁ − r₂ + (n − 1)t
Δφ = 2πΔ/λ · I/Imax = cos²(πΔ/λ)
S₁ is at +d/2 and S₂ at −d/2. Δ is optical path 1 minus optical path 2; positive Δ means wave 1 arrives with a phase delay. The plate term is zero when removed.
A coherent two-path model
Both slits have equal, constant scalar amplitude and the same fixed source phase. Exact geometric distances set every screen pixel. A plane plate at near-normal incidence adds (n − 1)t in arm 1 without changing the ray geometry. L = 1.50 m is fixed. λ is the vacuum/air wavelength; n is independently adjustable.
This model excludes dispersion, finite slit width and diffraction envelopes, inverse-distance amplitude changes, Fresnel reflections and multiple thin-film interference. Glass preserves the assumed coherence and equal amplitudes, so fringe visibility stays 100%.
Read the views
The apparatus is enlarged and separated for clarity. Coloured lines identify the two optical paths; they are not photon tracks, and both arms carry the same monochromatic light. The screen uses that wavelength's approximate colour. Its pixel intensity and plotted curve use the same I/Imax model.
The two wave traces and their sum show scalar oscillations at P, with E₂/A = cos θ and E₁/A = cos(θ − Δφ). Playback advances an arbitrary slowed phase, not optical time in seconds. The detector reports time-averaged intensity; instantaneous cancellation during an oscillation is different from a dark fringe.