Multiple Choice
In single-slit diffraction, which condition gives the angular position of the first minimum in the diffraction pattern on a distant screen?
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34. Wave Optics
Single Slit Diffraction
Multiple Choice
A single slit is illuminated by coherent monochromatic light at On a screen behind the slit, a central bright spot is observed to have a width of What is the width of the single slit?
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Verified step by step guidance1
Understand the problem: We are dealing with a single slit diffraction pattern, where the width of the central bright fringe is given, and we need to find the width of the slit.
Recall the formula for the width of the central maximum in a single slit diffraction pattern: \( W = \frac{2 \lambda L}{a} \), where \( W \) is the width of the central maximum, \( \lambda \) is the wavelength of the light, \( L \) is the distance from the slit to the screen, and \( a \) is the width of the slit.
Identify the given values: \( \lambda = 680 \text{ nm} = 680 \times 10^{-9} \text{ m} \), \( L = 2.9 \text{ m} \), and \( W = 39 \text{ mm} = 39 \times 10^{-3} \text{ m} \).
Rearrange the formula to solve for the width of the slit \( a \): \( a = \frac{2 \lambda L}{W} \).
Substitute the known values into the rearranged formula to find \( a \): \( a = \frac{2 \times 680 \times 10^{-9} \times 2.9}{39 \times 10^{-3}} \). Calculate this expression to find the width of the slit.
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