Two waves having intensities in the ratio of `16:1` produce interference. The ratio of maxium to minimum intensities is equal to

Options

A. `10:8`
B. `9:1`
C. `25:9`
D. `4:1`

Answer

C

Explanation

Ratio of intensities are given by
`(l_(1))/(l_(2))=(a_(1)^(2))/(a_(2)^(2))=16/1`
`implies (a_(1))/(a_(2))=sqrt(16/1)`
`implies(a_(1))/(a_(2))=4/1`
Then `(l_("max"))/(l_("min"))=((a_(1)+a_(2))^(2))`
`=((4+1)^(2))/((4-1)^(2))`
`=((5)^(2))/((3)^(2))=25/9`
Thus `l_("max"):l_("min")=25:9`