Two waves having the intensities in the ratio of `9 : 1` produce interference. The ratio of maximum to minimum intensity is equal to

Options

A. `10 : 8`
B. `9 : 1`
C. `4 : 1`
D. `2 : 1`

Answer

C

Explanation

We know that, `(l_(1))/(l_(2)) = (a_(1)^(2))/(a_(2)^(2)) = (9)/(1) rArr (a_(1))/(a_(2)) = sqrt((9)/(1))`
`rArr (a_(1))/(a_(2)) = (3)/(1)`
Then, `(l_("max"))/(l_("min")) = ((a_(1) + a_(2))^(2))/((a_(1) - a_(2))^(2)) = ((3 + 1)^(2))/((3-1)^(2)) = ((4)^(2))/((2)^(2)) = (16)/(4) = (4)/(1)`
Then, `l_("max") : l_("min") = 4 : 1`