In the Young's double-slit experiment, the interference pattern is found to have intensity ratio between gright and dark fringes as 9. This implies that
(i) the intensities at the screen due to the two slits are 5 units and 4 units respectively
(ii) the intensities st the screen due to the slits are 4 units and 1 unit respectively
(iii) the amplitude ratio is 3
(iv) the amplitude ratio is 2

Options

A. (i), (ii)
B. (ii), (iii)
C. (i), (iii)
D. (ii), (iv)

Answer

D

Explanation

`I_(max)/I_(min)=((sqrt(I_(1))+sqrt(I_(2)))/(sqrt(I_(1))~sqrt(I_(2))))^(2)=((sqrt(I_(1)//I_(2))+1)/(sqrt(I_(1)//I_(2))-1))^(2)=9/1`
`(sqrt(I_(1)//I_(2))+1)/(sqrt(I_(1)//I_(2))-1)=3 implies sqrt(I_(1)//I_(2))+1=3sqrt(I_(1)//I_(2))-3`
`2sqrt(I_(1)//I_(2))=4 impliessqrt(I_(1)/I_(2))=2 implies I_(1)/I_(2)=4`,
`I_(1)=4I^('),I_(2)=I^(')`, (ii) is O.K.
`I_(1)/I_(2)=4(a_(1)/a_(2))^(2) implies a_(1)/a_(2)=2`, hence, (iv) is O.K.`