For a single slit of width a, the first minimum of the interference pattern of a monochromatic light of wavelength l occurs at an angle of \frac{\lambda}{a}. At the same angle of \frac{\lambda}{a}, we get a maximum for two narrow slits separated by a distance a. Explain.

CBSE Class 12 Physics 2014 Delhi Set 1 Paper - Question 11

CBSE Class 12 Physics 2014 Delhi Set 1 Paper

Question : 11 of 30

Marks: +1, -0

For a single slit of width a, the first minimum of the interference pattern of a monochromatic light of wavelength

l

occurs at an angle of

\;{λ}/{a}

. At the same angle of

\;{λ}/{a}

, we get a maximum for two narrow slits separated by a distance a. Explain.

Solution:

When a single slit is used, the interference pattern is due to the diffraction phenomenon. Since, corresponding wavelets from two halves of a single slit have a path difference of

\;{λ}/{2}

., the overlapping of their contributions in the first scenario results in a minimum. Because these wavefronts have a path difference of

λ

in the second example, the overlapping of the wavefronts from the two slits results in the first maximum.

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