In a double-slit lab experiment, two slits are known to be 2.00 mm apart. A mixt

Question

In a double-slit lab experiment, two slits are known to be 2.00 mm apart. A mixture of two wavelengths of light shines simultaneously on the slits and this light is diffracted through the slits. The wavelengths are lambda1 = 750.0 nm and lambda 2 = 900.0 nm. The two interference patterns share a common central maximum. On a screen positioned 2.00 m from the slits, at what minimum distance from the central maximum will a bright fringe of one wavelength light coincide (overlap exactly) with a bright fringe of the other wavelength light?

Explanation / Answer

the minimum distance condition for two different wavelengths ie n th bright fringe of one falls on n+1 th bright fringe of other

(n+1)(Lambda)1 =(n)(Lambda)2 (n+1)(750)=n(900) (n+1)/n =6/5 n=5th bright fringe of 900nm waves coincide with 6th bright fringe of 750 nm waves

if the central fringe of pttern is at the origin then

the position of n th bright fringe xn=n'(Lambda1)D/d =6(750)(10)-9(2) /2(10)-3   xn=45cm

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