In Young's double slit interference experiment, using two coherent waves of different amplitudes, the intensities ratio between bright and dark fringes is 3 Then, the value of the wave amplitudes ratio that arrive there is

Options

A. `((sqrt(3)+1)/(sqrt(3)-1))`
B. `((sqrt(3)-1)/(sqrt(3)+1))`
C. `sqrt(3):1`
D. `1:sqrt(3)`

Answer

A

Explanation

According to given question
`I_(1):I_(2)=3:1, a_(1):a_(2)=?`
The intensity of light due to an illuminated slit is directly proportional to the width of the slit, if `w_(1)` and `w_(2)` be the width screen due to the respective slits then
`w_(1)/w_(2)=I_(1)/I_(2)=(a_(1)/a_(2))^(2)`
where `a_(1)` and `a_(2)` are the amplitude of the corresponding that wave
Here, `w_(1)/w_(2)=3/1rArr(a_(1)/a_(2))^(2)=3/1 or a_(1):a_(2)=sqrt(3):1`