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_2 cos phi)`
`phi=0, cos 0 = 1, A_("max") = sqrt(a_1^2 + a_2^2 + 2a_1 a_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`