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Question
Two coherent sources of light having intensity ratio 81 : 1 produce interference fringes. Calculate the ratio of intensities at the maxima and minima in the interference pattern.
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Solution
I1 : I2 81:1
If A1 and A2 are the amplitudes of the interfering waves, the ratio of the intensity maximum to the intensity minimum in the fringe system is
`I_max/I_max = ((A_1 +A_2)/(A_1-A_2))^2= ((r+1)/(r-1))^2`
where `r=A_1/A_2` Since the intensity of a wave is directly proportional to the square of its amplitude,
`I_1/I_2=(A_1/A_2)^2=r^2`
`therefore r = sqrt(I_1/I_2)=sqrt81=9`
`therefore I_max/I_max =((9+1)/(9-1))^2=(10/8)^2=(5/4)^2=25/16`
∴ The ratio of the intensities of maxima and minima in the fringe system is 25 : 16.
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