Past exam of the physics 2 paper of the University of Oxford / 2013 / 4 / 2

For the centred screen, $|y|\le 0.30$ m. Retaining the screen-angle geometry givesThere are about $\bar{\sigma }{\Delta }_{\max }=10.045$ carrier orders on each side. With equal spectral intensities, direct extrema of the intensity formula giveTheir contrast declines toward the edges: the first equal-intensity visibility zero occurs at $\Delta =1/(2\Delta \sigma )=5.25\mu \mathrm{m}$, just beyond the screen's $5.145\mu \mathrm{m}$ limit. Edge visibility is only about $0.031$, so fewer fringes may be discernible at a practical contrast threshold.

The screen reaches $|y|/D=0.6$, where a paraxial conversion of its full width is inaccurate. Also, wavelength-independent detector sensitivity does not itself establish equal source intensities. The boxed count specifies the usual equal-intensity idealization; without spectral weights and a visibility threshold, a unique experimental count is not fixed.