 Solution

ID: 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} = 2 A_{1}

. The local interference extrema are

(A_{1} + A_{2})^{2}

and

(A_{2} - A_{1})^{2}

\frac{I _{m a x}}{I _{m i n}} = \frac{( 1 + 2 ) ^{2}}{( 2 - 1 ) ^{2}} = 9.

These are the central-envelope extrema as relative phase varies, or equivalently the near-centre fringe limits where the envelope is nearly constant.

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