Question

# In young's double slit experiment β is the fringe width and Io is the intensity of the central bright fringe. What will be the intensity at a distance x from the central bright fringe?

A
Io cos (xβ)
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B
Io cos2(xβ)
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C
Io cos2(πxβ)
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D
(Io4) cos2πxβ
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Solution

## The correct option is A Io cos2(πxβ)If δ is the phase difference between two waves with intensities I1 and I2, then the total intensity is given byI=I1+I2+2√I1I2cosδAt the central fringe, the phase difference, δ=0. Also given Io as the intensity of central bright fringe.Hence we have,I=I1+I2+2√I1I2Also for the points between maxima and minima, I1=I2=I1Therefore Io=I1+I1+2I1=4I1⟹I1=Io4Now at distance x from the center, the path difference = πxDTherefore phase difference, δ=2πλπxDHence intensity at that point is given byI′=I1+I1+2I1cos2πxdλDi.e, I′=Io4+Io4+2Io4cos2πxdλD⟹I′=Io2[1+cos2πxdλD]⟹I′=Iocos2πxdλD [2cos2x=1+cos2x]Also we have, fringe width β=λDdHence we have, I′=Iocos2πxβ

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