A single-slit diffraction pattern is formed on a distant screen. If the width of the single slit through which light passes is reduced, what happens to the width of the central bright fringe? Assume the angles involved remain small.A. The central bright fringe becomes wider. B. The central bright fringe remains the same size. C. The effect cannot be determined unless the distance between the slit and the screen is known.
D. The central bright fringe becomes narrower.

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aristocles aristocles · Answer 1 · 2019-11-13T02:27:09+01:00

Answer:

A. The central bright fringe becomes wider.

Explanation:

Width of central bright fringe is given by the formula

[tex]a sin\theta = N\lambda[/tex]

now for position of first minima on both sides of central bright fringe is given as

[tex]\theta = \pm \frac{\lambda}{a}[/tex]

so the angular width of central maximum is given as

[tex]\beta = 2\theta[/tex]

[tex]\beta = 2\frac{\lambda}{a}[/tex]

now width of maximum is given as

[tex]w = \frac{2L\lambda}{a}[/tex]

now we can see that this width is inversely depends on the width of slit

so on decreasing the slit width the central maximum width must have to increase