A beam of light of a single wavelength is incident...

A beam of light of a single wavelength is incident perpendicularly on a double-slit arrangement, as in Fig. $35-10 .$ The slit widths are each 46$\mu \mathrm{m}$ and the slit separation is 0.30 $\mathrm{mm} .$ How many complete bright fringes appear between the two first-order minima of the diffraction pattern?

A beam of light of a single wavelength is incident perpendicularly on a double-slit arrangement, as in Fig. $35-10 .$ The slit widths are each 46$\mu \mathrm{m}$ and the slit separation is 0.30 $\mathrm{mm} .$ How many
complete bright fringes appear between the two first-order minima
of the diffraction pattern?

Key Concepts

Superposition of Diffraction and Interference Patterns

In many optical experiments the diffraction pattern produced by each individual slit serves as an envelope on which the finer interference fringes, due to the two slits, are superimposed. This means that even though double-slit interference produces many fringes, only those that fall within the relatively wide diffraction envelope’s regions of high intensity (i.e., between its minima) are clearly visible.

Fringe Visibility and Limiting Effects of Diffraction Minima

The number of observable bright fringes is influenced by the positions of the diffraction minima. In combined interference-diffraction situations, the interference fringes that fall outside the main diffraction envelope (bounded by the diffraction minima) are suppressed. Thus, counting the bright fringes between specific diffraction minima requires understanding how the diffraction envelope limits the region where interference is visible.

Single?Slit Diffraction

When light passes through a narrow slit, it does not travel in a perfectly straight line but instead spreads out, creating a diffraction pattern characterized by a central bright region and several minima and secondary maxima. The positions of these minima are determined by the width of the slit and the wavelength of light, forming an envelope that modulates any superimposed interference pattern.

Young's Double?Slit Interference

This concept explains that when coherent light passes through two closely spaced slits, the emerging wavefronts overlap and interfere. Constructive interference (where the waves are in phase) produces bright fringes, while destructive interference (out of phase) produces dark fringes on the observation screen. The regular spacing of these fringes is determined by the slit separation and the wavelength of the light.

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