Question

The ratio of maximum and minimum intensities in an interference pattern is 36 : 1. What is the ratio of the amplitudes of the two interfering waves?

Answer 1

${\displaystyle \frac{{\text{I}}_{\text{max}}}{{\text{I}}_{\text{min}}}=\frac{36}{1}}$

${\displaystyle \frac{{\text{I}}_{\text{max}}}{{\text{I}}_{\text{min}}}=\frac{{({\text{a}}_1+{\text{a}}_2)}^2}{{({\text{a}}_1-{\text{a}}_2)}^2}}$

${\displaystyle \frac{{({\text{a}}_1+{\text{a}}_2)}^2}{{({\text{a}}_1-{\text{a}}_2)}^2}=\frac{36}{1}=\frac{6^2}{1^2}}$

${\displaystyle \frac{{\text{a}}_1+{\text{a}}_2}{{\text{a}}_1-{\text{a}}_2}=\frac{6}{1}}$

a₁ + a₂ = 6a₁ - 6a₂

a₂ + 6a₂ = 6a₁ - a₁ 

7a₂ = 5a₁ 

${\displaystyle \frac{7}{5}=\frac{{\text{a}}_1}{{\text{a}}_2}}$

a₁ : a₂ = 7 : 5