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If one of tow identical slits producing interference in Young's expeiment is covered with glass, so that the light intensity passing through it is reduced to 50% , find the ratio of the maximum and minimum intensity of the fringe in the interence pattern.

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Let the amplitudes of the light waves passing through the slits be `a_(1)` and `a_(2)` and the corresponding intensities be `I_(1)` and `I_(2)`.
According to the problem,
`I_(2)= 0.5 I_(1) = I_(1)/(2)`
`:. a_(2)^(2) =(a_(1)^(2))/(2) [because O prop a^(2)]`
or `a_(2)= (a_(1))/(sqrt(2))`
`:. I_("max")/I_("min")=(a_(1)+a_(2))^(2)/((a_(1)-a_(2))^(2))=((a_(1)+a_(1)/sqrt(2))/(a_(1)-a_(1)/sqrt(2)))^(2)=((1+1/sqrt(2))/(1-1/sqrt(2)))^(2)`
`=((sqrt(2)+1)/(sqrt(2)-1))^(2)~~34`
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