Question

2 coherent sources whose intensity ratio is 81:1 produce interference fringe. calculate ratio of intensity of maxima and minima in fringe system

Answer 1

Answer: The ratio of the intensity of maxima and minima is 25:16.

Explanation:

Given that,

Ratio of intensity $\dfrac{I_{1}}{I_{2}} = \dfrac{81}{1}$

We know that,

The intensity of maxima is

$I_{max} = (\sqrt{I_{1}}+\sqrt{I_{2}})^{2}$...(I)

Put the value of $I_{1}$ and $I_{2}$ in equation (I)

$I_{max} = 100$

The intensity of minima

$I_{min} = (\sqrt{I_{1}}-\sqrt{I_{2}})^{2}$....(II)

Put the value of $I_{1}$ and $I_{2}$ in equation (II)

$I_{min} = 64$

Now, the ratio of the intensity of maxima and minima

$\dfrac{I_{max}}{I_{min}}= \dfrac{100}{64}$

$\dfrac{I_{max}}{I_{min}}= \dfrac{25}{16}$

Hence, the ratio of the intensity of maxima and minima is 25:16.

Answer 2

"To determine: The ratio of the intensity of maxima and minima  when two coherence sources produce interference fringe

Given : The intensity ratio of two coherent sources is 81:1

Formula:

Intensity of $Maxima: I_{max} = (\sqrt{I_1}+\sqrt{I_2}) ^2$

Intensity of Minima: $I_{min} = (\sqrt{I_1}-\sqrt{I_2})^2$

Calculation

Ratio of intensity$\frac {I_1}{I_2} =\frac {81}{1}$

Let $I_1=81I,I_2=I$

Finding the intensity of maxima by formula

$I_{max} = (\sqrt{I_1}+\sqrt{I_2}) ^2$

$=  (\sqrt{81I}+\sqrt{I})^2$

$= 100I^2$

Finding the intensity of minima by formula

$I_{min} = (\sqrt{I_1}-\sqrt{I_2}) ^2$

$=  (\sqrt{81I}-\sqrt{I})^2$

$= 64I^2$

Ratio of intensity of maxima and minima = 100/64=25/16"