A student investigates the dependence of fringe width β on the inverse of slit separation 1/d in a Young’s double–slit set-up, keeping the wavelength λ and the slit–to–screen distance D fixed.
(a) Starting from the standard formula for β, express β as a linear function of 1/d and identify the theoretical slope.
(b) Draw a qualitative sketch of the graph of β versus 1/d and mark the intercept on the β-axis.
(c) For λ=650nm and D=1.2m, calculate the numerical value of the slope predicted by theory (in SI units).
(d) In an actual experiment the measured slope is found to be 7.6mm2. Suggest any two experimental factors that could cause this result to differ from the theoretical prediction.