For 640 nm light and slit separation 0.200 mm, measured (screen distance in m, fringe spacing in mm) data are (0.4, 1.28), (0.5, 1.6), (0.6, 1.92), (0.7, 2.24), (0.8, 2.56). (a) Find graph gradient and slit separation. (b) Compare with stated value. (c) Predict spacing at 1.20 m. (d) Explain covering one slit and reducing wavelength. (e) Explain multi-fringe measurement and a control.

Question

Accepted Answer

Gradient 3.20 mm/m gives slit separation 0.200 mm; predicted spacing at 1.20 m is 3.84 mm. From w = λD/a, gradient of w against D is λ/a. Endpoint gradient = (2.56 − 1.28)/(0.80 − 0.40) = 3.20 mm/m = 3.20 × 10⁻³. Thus a = λ/gradient = 640 × 10⁻⁹/(3.20 × 10⁻³) = 2.00 × 10⁻⁴ m = 0.200 mm, agreeing with the stated spacing. At D = 1.20 m, w = gradient × D = 3.20 × 1.20 = 3.84 mm. Covering one slit removes two-source interference, leaving a single-slit diffraction pattern. Reducing wavelength reduces fringe spacing directly if geometry is fixed. Measure across n fringe gaps then divide by n, reducing fractional ruler uncertainty. Keep wavelength, slit separation and screen alignment fixed while changing D.

Double-slit gradient and measurement design

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Fringe spacing against screen distance

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Fringe spacing against screen distance — supplied values
Screen distance / m	Fringe spacing / mm
0.4	1.28
0.5	1.6
0.6	1.92
0.7	2.24
0.8	2.56