 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/b/solution

A slit of width

w

has its first zeros at

sin θ = \pm λ / w

. Thus the full central-envelope widths are

W_{1} ≃ \frac{2 L λ}{w _{1}} = \frac{L}{10}, W_{2} ≃ \frac{2 L λ}{w _{2}} = \frac{L}{20} .

The narrower envelope determines the overlap, so it spans

\frac{W _{2}}{δ x} = 50 fringe spacings .

This is the usual approximate “50 fringes” count. If counting nominal bright fringe centres strictly inside both first zeros, they have indices

- 24, \dots, 24

, giving 49 centres. The endpoints

\pm 25

lie at the wider slit's first zeros, where two-slit visibility vanishes; they should not be counted as fully interfering bright centres.

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