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Chapter 5: Q46P (page 1214)

Coherent monochromatic light of wavelength 位passes through a narrow slit of width a, and a diffraction pattern is observed on a screen that is a distance x from the slit. On the screen, the width w of the central diffraction maximum is twice the distance x. What is the ratio a/位of the width of the slit to the wavelength of the light?

Short Answer

Expert verified

The ratio of the width of the slit to the wavelength of the light


Step by step solution

01

Central maximum

The separation between the two first-order (m=1, -1) minima, i.e., dark lines, is the width w of the central maximum. As a result, the distance between the center of the central maximum and the first dark line is w/2. if the first dark line intersects the central maximum at an angle

The equation is;

02

Ratio of the width of the slit to the wavelength of the light

The distance between the slit and the screen x=w/2;

Therefore,

Hence, the ratio of the width of the slit to the wavelength of the light

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