In YDSE, two wavelengths of `500 nm and 700 nm` are used. What is the minimum their maxima coincide ? Take `D//d = 10^(3)`, symbols have standard meaning.
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Here, `lambda_(1) = 500 nm, lambda_(2) = 700 nm` Let `n_(1)th` maximum of `lambda_(1)` coincide with `n_(2)th` maximum of `lambda_(2)` `:. n_(1)(lambda_(1) D)/(d) = n_(2)(lambda_(2)D)/(d)` `(n_(1))/(n_(2)) = (lambda_(2))/(lambda_(1)) = (700)/(500) = (7)/(5)` `:.` `7th` maximum corresponding to `500 nm` coincides with `5th` maximum corresponding to`700nm`. After this, `14th` max. of `lambda_(1)` will coincide with `10th` max. of `lambda_(2)`. Hence the minimum distance from the central maximum, where the maxima due to two wavelengths coincide is `y_(1) = n_(1)(lambda_(1)D)/(d) = 7 xx (500 xx 10^(-9)) xx 10^(3)` `= 3.5 xx 10^(-3)m y = 3.5 mm`.
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