When waves from two coherent source of amplitudes a and b superimpose , the amplitude R of the resultant wave is given by R = `sqrt(a^(2)+b^(2)+2ab cos phi). `
where `phi` is the constant phase angle between the two waves. The resultant intensity I is directly proportional to the square of the amplitude of the resultant wave i.e `I prop R^(2)` i.e,
`I prop (a^(2) +b^(2) +2ab cos phi )`
For constructive interference ,
`phi = 2n pi " ""and"" " I _("max") = (a+b)^(2)`
For destructive interference ,
`phi = (2n-1) pi "and" I_("min") = (a-b)^(2)`
If `I_(1) I_(2)` are intensities from two slits of width `w_(1) "and" w_(2) ` then
`I_(1)/I_(2)=w_(1)/w_(2)=a^(2)/b^(2)`
Light waves from two coherent sources of intensity ratio 81 : 1 produce interference. With the help of the passage choose the most appropriate alternative for each of the following questions
If two slits in Young's experiment have width ratio 1:4 the ratio of maximum and minimum intensity in the interference pattern would be

Options

A. 1 : 4
B. 1 : 16
C. 9 : 1
D. 9 : 16

Answer

A