Answered

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Monochromatic light of wavelength lambda, such as light from a laser, is directed through two narrow parallel slits that are a distance d apart. There is a viewing screen a very long distance R away from the slits that is used to observe the interference pattern that emerges from the light shining through the slits. The distance that light travels from one slit to the screen is r1 and the distance that light travels from the other slit to the screen is r2. The central bright fringe of the interference pattern results due to a path difference, r1 – r2, of zero. What path difference is required to produce the first order bright fringe that is adjacent to the central bright fringe?

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Answer:

When r1 – r2 equal the wavelength of the monochromatic light

Explanation:

This is because to observe a bright fringe a constructive interference pattern of path difference, r1 – r2 = mλ is observed, where m is an integer and λ = wavelength of monochromatic light.

For bright fringes and thus constructive interference, r1 – r2 must be integral multiples of the wavelength, λ. When r1 – r2 , we have the central bright fringe and thus m = 0.

The first order bright fringe which is adjacent to the central bright fringe is obtained when m = 1,

So r1 – r2 = 1 × λ

r1 – r2 = λ

Thus, the path difference required to produce the first order bright fringe that is adjacent to the central bright fringe is when r1 – r2 = λ, the wavelength of the monochromatic light.

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