34. Wave Optics
Young's Double Slit Experiment
3:39 minutes
Problem 33d
Textbook Question
Textbook QuestionFIGURE CP33.73 shows two nearly overlapped intensity peaks of the sort you might produce with a diffraction grating (see Figure 33.9b). As a practical matter, two peaks can just barely be resolved if their spacing Δy equals the width w of each peak, where w is measured at half of the peak’s height. Two peaks closer together than w will merge into a single peak. We can use this idea to understand the resolution of a diffraction grating. a. In the small-angle approximation, the position of the m=1 peak of a diffraction grating falls at the same location as the m=1 fringe of a double slit: y1=λL/d. Suppose two wavelengths differing by Δλ pass through a grating at the same time. Find an expression for Δy, the separation of their first-order peaks.
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