Question

obtain the expression for the ratio of intensities at maxima and minima in an interference pattern.

Answer 1

l'+l"/l'-l" is the answer

Answer 2

Question: Obtain the expression for the ratio of intensities at maxima and minima in an interference pattern.

Solution: Suppose $a_ 2$ and $a_2$ be the amplitudes and $I_1$ and $I_2$ the intensities of light waves which interfere each other

Intensity $\alpha$ $(Amplitude)^{2}$

$\frac{I_1}{I_2} =\frac{a_1}{a_2}$

After interference (applying superposition principle)

Amplitude at maxima $=a_1+a_2$

Amplitude at minima $=a_1-a_2$

$\frac{1max}{1min}=\frac{(a_1+a_2)^{2} }{(a_1+a_2)^{2} }$

$\frac{1max}{1min} =\frac{(\frac{a_1}{a_2 }+1)^{2} }{(\frac{a_1}{a_2}+1 )^{2} } =(\frac{r+1}{r-1} )^{2}$

Where r  $=\frac{a_1}{a_2} =\sqrt{\frac{I_1}{I_2} } =$ amplitude ratio of two waves.