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A fellow student, who values memorizing equations above understanding them, combines Eq. (35.4) and (35.13) to 鈥減rove鈥 that can only equal localid="1663905625404" 2m. How would you explain to this student that can have values other than localid="1663906387916" 2m?

Short Answer

Expert verified

If is not an integral multiple of, constructive interference will not take place. the value ofcan be anything, but we only need to consider those for which,mis an integer.

Step by step solution

01

Define the principle of superposition.

The essential condition for the occurrence of constructive interference at any point is that the path difference between the rays, moving towards the point, is equal to the integral multiple of the wavelength of light used.

Similarly, for destructive interference, the path difference should be half-integral multiple of the wavelength of light.

02

Determine the values of ∅.

The path difference in multiple diffractions is equal to mi.e.,=m.

By trigonometry, =d蝉颈苍胃. Now,

=2=2dsin=2m=2蟺尘m=0.+2,+3,

This equation will work only for special cases where is an integer multiple of the wavelength and the value ofwill not be limited to these values

Hence, the value ofcan be anything but we need to consider only those for which is an integral multiple of ,.

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