Two coherent light sources of intensity ratio 25 : 4 are employed in an interference experiment what is the ratio of the intensities of the maxima and minima in the interference pattern?

Solution

Let I₁ and I₂ be the intensities of the two coherent beams and A₁ and A₂ their respective amplitudes.

Now given,
Intensity ratio,

\frac{I_{1}}{I_{2}} = \frac{25}{4},

therefore,

\frac{A_{1}}{A_{2}} = \sqrt{\frac{I_{1}}{I_{2}}}

Amplitude ratio ,

\frac{A_{1}}{A_{2}} = \sqrt{\frac{25}{4}} = \frac{5}{2}

i.e.,

A_{1} = 5 units

and,

A_{2} = 2 units

At maxima : A_{\max} = A_{1} + A_{2} = 7 units At minima : A_{\min} = A_{1} - A_{2} = 3 units

Hence,

\frac{I_{\max}}{I_{\min}} = \frac{A_{\max}^{2}}{A_{\min}^{2}}

\Rightarrow

\frac{I_{\max}}{I_{\min}} = \frac{(7)^{2}}{(3)^{2}}

\Rightarrow

I_{\max} : I_{\min} = 49 : 9

is the ratio of intensities of the maxima and minima in the interference pattern.

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