Question

Two waves have intensities in the ratio 1 : 9. If these waves produce interference, then ratio of maximum and minimum intensities is

A ) 3 : 1

B ) 4 : 1

C ) 9 : 1

D ) 16 : 1

Answer 1

The correct option is (B) 4 : 1.

I₁ = 1

I₂ = 9

I_max = (√I₂ + √I₁)²

I_min = (√I₂ - √I₁)²

\(\frac{I_{max}}{I_{min}}=\frac{(\sqrt{I_2}+\sqrt{I_1})^2}{(\sqrt I_2-\sqrt I_1)^2}\)

\(\frac{I_{max}}{I_{min}}=\frac{(\sqrt{9}+\sqrt{1})^2}{(\sqrt 9-\sqrt 1)^2}\) 

\(\frac{I_{max}}{I_{min}}=\frac{(3+1)^2}{(3-1)^2}\) 

\(\frac{I_{max}}{I_{min}}=\frac{(4)^2}{(2)^2}\) 

^{\(\frac{I_{max}}{I_{min}}=\frac{16}{4}\)} 

\(\frac{I_{max}}{I_{min}}=\frac4{1}\)