Two light sources with amplitudes 5 units and 3 units respectively interfere with each other. Calculate the ratio of maximum and minimum intensities.

Explanation

Amplitudes , `a_1=5 , a_2=3`
Resultant amplitude, `A=sqrt(a_1^2+a_2^2+2a_1a_2cos phi)`
Resultant amplitude is maximum when,
`phi=0, cos 0 =1 , A_"max"=sqrt(a_1^2+a_2^2+2a_1a_2)`
`A_"max"=sqrt((a_1+a_2)^2)=sqrt((5+3)^2)=sqrt((8)^2)`=8 units
Resultant amplitude is minimum when , `phi =pi , cos pi =-1 , A_"max"=sqrt(a_1^2+a_2^2-2a_1a_2)`
`A_"min"=sqrt((a_1-a_2)^2)=sqrt((5-3)^2)=sqrt((2)^2)`=2 units
`I prop A^2`
`I_"max"/I_"min"=(A_"max")^2/(A_"min")^2`
Substituting, `I_"max"/I_"min"=(8)^2/(2)^2=64/4=16` (or) `I_"max":I_"min"=16:1`