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  • Two coherent sources separated by distance d are radiating in phase having wavelength  A detector mo

Two coherent sources separated by distance d are radiating in phase having wavelength \lambda. A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of \mathrm{n=4 } interference maxima is given as:

Option: 1

\mathrm{\sin ^{-1} \frac{n \lambda}{d}}


Option: 2

\mathrm{\cos ^{-1} \frac{4 \lambda}{\mathrm{d}}}


Option: 3

\mathrm{\tan ^{-1} \frac{d}{4 \lambda}}


Option: 4

\mathrm{\cos ^{-1} \frac{\lambda}{4 \mathrm{~d}}}


Answers (1)

best_answer

Path difference at a point Q on the circle is

\mathrm{ \Delta y=d \cos \theta }                    (i) 

For maxima at Q path difference should be integer multiple of wavelength 

\mathrm{\Delta \mathrm{y}=\mathrm{n} \lambda}          (ii)

From eqs. (i) and (ii),

\mathrm{\mathrm{n} \lambda=\mathrm{d} \cos \theta}

\mathrm{\therefore \quad \theta=\cos ^{-1}\left(\frac{\mathrm{n} \lambda}{\mathrm{d}}\right)}
For \mathrm{\quad \mathrm{n}=4}

Angular position, \mathrm{\theta=\cos ^{-1}\left(\frac{4 \lambda}{\mathrm{d}}\right)}

Posted by

Pankaj Sanodiya

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