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652.


Problem 46.5 (RHK)


A single slit is illuminated by light whose wavelengths are and , so chosen that the first diffraction minimum of the component coincides with the second minimum of the component. (a) We have to find the relationship that exists between the two wavelengths. (b) We have to find whether there are any other minima in the two patterns that coincide.


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(a)

The condition for diffraction minima in a single slit diffraction is

It is given that the first diffraction minimum of the component coincides with the second minimum of the component. Therefore, we obtain the following relation by applying these conditions;

.

(b)

For answering the second part of the problem, we will determine integers and such that

We find that the fourth minimum of will coincide with the second minimum of , and so on.