Two-Slit Interference with a Real Source
A student sets up a double slit with separation 0.25 mm and observes fringes on a screen 1.80 m away using a red laser labeled 650 nm. The measured fringe spacing is 4.2 mm, but the fringes are washed out near the edges of the pattern and the central maximum is noticeably dimmer than expected. The student also notices that when a piece of ordinary white light is substituted, colored fringes appear only near the center. A classmate suggests increasing the slit separation to sharpen the fringes.
1. Use the measured spacing to check the slit separation and comment on the consistency.
Read the worked answer
For small angles, fringe spacing is Δy = λ L / d, so d = λ L / Δy = (650e-9 * 1.80) / (4.2e-3). Numerator: 650e-9 * 1.80 = 1.17e-6. Divide by 4.2e-3 gives 2.79e-4 m = 0.279 mm.
The measured spacing implies d ≈ 0.28 mm, close to the stated 0.25 mm (about 11% high). That is within plausible measurement error on the spacing, but the student should quote the uncertainty. If d = 0.25 mm exactly, the expected spacing is Δy = 1.17e-6 / 2.5e-4 = 4.68 mm, which is about 11% larger than measured. The discrepancy is small but should be reported, not ignored.
2. Explain why the fringes are washed out and why white light gives color only near the center.
Read the worked answer
Both effects come from coherence and path difference, not from the slit separation.
- Washed-out fringes: real sources have finite spatial and temporal coherence. As the path difference grows toward the edge of the pattern, the fringe visibility falls because the source is not perfectly monochromatic (finite coherence length) and has finite width. The envelope of the pattern is set by single-slit diffraction; the central maximum dimming suggests the slits are not equally illuminated or are wider than assumed.
- White light: different wavelengths give different fringe spacings, so fringes of different colors overlap and wash out at higher orders. Only near the center (small path difference) do the orders coincide, giving a white central fringe flanked by colored fringes. This is a coherence-length effect, not a slit-separation effect.
3. Evaluate the classmate's suggestion to increase the slit separation.
Read the worked answer
Increasing d decreases the fringe spacing (Δy = λL/d), making the fringes harder to resolve, not sharper. It also narrows the single-slit diffraction envelope only if slit width changes; if only separation changes, the envelope is unchanged but the fringes crowd together.
To sharpen fringes the student should instead: use a more monochromatic and spatially coherent source, reduce stray light, ensure equal slit illumination, and increase L (which increases spacing). Increasing d is the wrong direction. The suggestion confuses 'sharper' (better visibility/contrast) with 'more separated' (larger spacing).