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Chapter 5: Q11E (page 1212)

Red light of wavelength 633 nm from a helium-neon laser passes through a slit 0.350 mm wide. The diffraction pattern is observed on a screen 3.00 m away. Define the width of a bright fringe as the distance between the minima on either side.

(a) What is the width of the central bright fringe?

(b) What is the width of the first bright fringe on either side of the central one?

Short Answer

Expert verified
  1. The width of the central bright fringe is 10.84 mm.
  2. The width of the first bright fringe on either side of the central one is 5.42 mm.

Step by step solution

01

Given.

位=633nm=633脳10-9m,a=0.350mm=0.350脳10-3m,R=3.00m

02

Calculate the width of the first bright fringe on either side of the central one

We are given with the sit separation d = 0.350 mm, the distance from slits to screen D =3 m, and the wavelength位=633nm. So for the width of the first bright fringe on either side of the central one

dsin胃=m位(1)

For smaller 胃,sin胃鈮�胃the equation is

胃=yD

By substituting the value ofin equation (1), we get

dyD=m位y=(m)(位)(D)d=(位)(D)dm=1incaseofcentralbrightfringe=(633脳10-9)(3)0.350脳10-3=5.42脳10-3m=5.42mm

03

Calculate the width of the central bright fringe.

The width of the central bright fringe will be 2y of the first bright fringe on either side of the central one. So

2y=2脳5.42mm=10.84mm

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