Why is the following situation impossible? A technician is...

Why is the following situation impossible? A technician is sending laser light of wavelength $632.8 \mathrm{nm}$ through a pair of slits separated by $30.0 \mu \mathrm{m}$. Each slit is of width $2.00 \mu \mathrm{m}$. The screen on which he projects the pattern is not wide enough,so light from the $m=15$ interference maximum misses the edge of the screen and passes into the next lab station, startling a coworker.

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Key Concepts

Double-Slit Interference

Double-slit interference arises when coherent waves emanating from two narrow and closely spaced slits produce a pattern of alternating bright and dark fringes due to constructive and destructive interference. The positions of the bright fringes are determined by the condition that the path difference between the two slits is an integral multiple of the wavelength.

Single-Slit Diffraction

Single-slit diffraction refers to the spreading of light as it passes through a narrow aperture, producing an intensity envelope characterized by a central maximum and successive minima. The positions of these minima depend on the wavelength of the light and the width of the slit, setting boundaries on the observable intensity distribution.

Interference-Diffraction Overlap and Missing Orders

In a double-slit experiment, the overall light pattern is the product of the double-slit interference pattern and the single-slit diffraction envelope. When an interference maximum coincides with a diffraction minimum, it is effectively 'missing' because the diffraction envelope nullifies the intensity at that point. In this context, if the m=15 interference maximum falls at or beyond the edge of the diffraction envelope, it cannot form as a bright fringe, rendering the described scenario impossible.

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