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A slit of width 0.6 mm is illuminated by a beam of light consisting of two wavelengths 600 nm and 480 nm. The diffraction pattern is observed on a screen 1.0 m from the slit. Find:

(i) The distance of the second bright fringe from the central maximum pertaining to light of 600 nm.

(ii) The least distance from the central maximum at which bright fringes due to both the wavelengths coincide.

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(i) \(x =\frac{n\,\lambda \,D}{d}\)

\(x = \frac{2\times600\times1}{0.6\times10^{-3}}\)

x = 2000 x 103

x = 2 x 106 nm

(ii) we consider that nth bright fringe of \(\lambda\) and (n -1)th bright fringe of wavelength \(\lambda_1\) consider with each other

\(n\lambda_2 = (n -1)\lambda_1\)

480n = (n - 1) 600

480n = 600n - 600

600 = 120n

n = \(\frac{600}{120}\)

n = 5

The least distance from the central maxima 

\(x' = n\lambda_2\frac Dd\)

\(x' = 5\times\frac{480\times1}{0.6\times10^{-3}}\)

x' = 400 x 103

x' = 4 x 106 nm

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