Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2014 / Paper 1 / B7 / c / Solution

At the centre, equal illumination gives slit amplitudes proportional to widths, so $A_2=2A_1$. The local interference extrema are $(A_1+A_2{)}^2$ and $(A_2-A_1{)}^2$, givingThese are the central-envelope extrema as relative phase varies, or equivalently the near-centre fringe limits where the envelope is nearly constant.