In an interference pattern, the ratio of maximum intensity to minimum intensity is 25:1. Find the ratio of the amplitudes and intensities of the two interfering waves.

Explanation

We have `(I_("max"))/(I_("min"))=((a_(1)+a_(2))^(2))/((a_(1)-a_(2))^(2))=25/1=((a_(1)+a_(2))^(2))/((a_(1)-a_(2))^(2))`
`:.(a_(1)+a_(2))/(a_(1)-a_(2))=5/1`
`5a_(1)-5a_(2)=a_(1)+a_(2)" "4a_(1)=6a_(2)" "(a_(1))/(a_(2))=6/4=3/2`
As `I_(1)prop a_(1)^(2)` and `I_(2) prop a_(2)^(2)`
`(I_(1))/(I_(2))=(a_(1)^(2))/(a_(2)^(2))=(3/2)^(2)=9/4" "I_(1):I_(2)=9:4`