In a double-slit experiment the slit separation is 0.500 mm and the screen is 2.00 m away. Bright-fringe readings are (order relative to centre, position in mm): (-2, -4.08), (-1, -2.04), (0, 0), (1, 2.04), (2, 4.08). Use x = λD/a for adjacent-fringe spacing. (a) Determine wavelength using the two outer readings. (b) Predict the new spacing when slit separation is doubled. (c) Explain coherence and one measurement improvement.

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Wavelength 5.1e-7 m (510 nm); new spacing 1.02 mm; measure several fringe intervals from a coherent source. There are four adjacent intervals between orders −2 and +2. Their total separation is 8.16 mm, giving x = 8.16/4 = 2.04 mm = 0.00204 m. Rearrange x = λD/a to λ = xa/D. Convert a = 0.500 mm = 5.00 × 10⁻⁴ m, then λ = 0.00204 × 5.00 × 10⁻⁴/2.00 = 5.1e-7 m. With the same wavelength and screen distance, spacing is inversely proportional to slit separation. Doubling a therefore halves the spacing to 1.02 mm; it does not change the emitted wavelength. Coherent waves have a constant phase difference and the same frequency, maintaining stable interference fringes. Measure across many intervals and repeat to reduce fractional position error. Keep the screen normal to the central beam and avoid looking directly into a laser source.

Wavelength from double-slit fringes 4

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Bright-fringe positions

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Bright-fringe positions — supplied values
Fringe order	Position / mm
-2	-4.08
-1	-2.04
0	0
1	2.04
2	4.08