Question

the intensity ratio of two coherent waves is 4:1. if they produce interference, the ratio of maximum to minimum intensity will be​

Answer 1

The intensity ratio,

$\sf{\longrightarrow\dfrac{I_1}{I_2}=\dfrac{4}{1}}$

If $\sf{A_1}$ and $\sf{A_2}$ are amplitudes respectively,

$\sf{\longrightarrow\left(\dfrac{A_1}{A_2}\right)^2 =\dfrac{4}{1}}$

$\sf{\longrightarrow\dfrac{A_1}{A_2}=\dfrac{2}{1}}$

We see $\sf{A_1>A_2.}$

When they produce interference, the ratio of maximum to minimum amplitudes will be,

$\sf{\longrightarrow\dfrac{A_1'}{A_2'}=\dfrac{A_1+A_2}{A_1-A_2}}$

$\sf{\longrightarrow\dfrac{A_1'}{A_2'}=\dfrac{2+1}{2-1} }$

$\sf{\longrightarrow\dfrac{A_1'}{A_2'}=\dfrac{3}{1} }$

Hence the ratio of maximum to minimum intensities will be,

$\sf{\longrightarrow\dfrac{I_1'}{I_2'}=\left(\dfrac{A_1'}{A_2' }\right)^2}$

$\sf{\longrightarrow\underline{\underline{\dfrac{I_1'}{I_2'}=\dfrac{9}{1}}}}$