Interference fringes are obtained due to the interference of wave from two coherent sources of light with amplitudes `a_(1)` and `a_(2)(a_(1)=2a_(2))`. The ratio of the maximum and minimum intensities of light in the interference pattern is

Options

A. 2
B. 4
C. 9
D. `oo`

Answer

C

Explanation

Intensity `prop (amplitude)^(2)`
`I_(1) prop a_(1)^(2),I_(2) prop a_(2)^(2)`
`I_(1)/I_(2)=(a_(1)/a_(2))^(2)=((2a_(2))/a_(2))=4`
`I_(1)=4I^('), I_(2)=I^(')`
`I_(max)/I_(min)=((sqrt(I_(1))+sqrt(I_(2)))/(sqrt(I_(1))~sqrt(I_(2))))^(2)`
`=((sqrt(4I^('))+sqrt(I^(')))/(sqrt(4I^('))-sqrt(I^('))))=(3/1)^(2)=9/1`