Question
The intensity variation in the interference pattern obtain with the help of two coherent sources is $5\%$ of the average intensity. Find out the ratio of intensities of two sources
✓
Answer
$\frac{{{{[\sqrt {{{\rm{I}}_1}} + \sqrt {{{\rm{I}}_2}} ]}^2} = (1.05){{\rm{I}}_{\rm{m}}}\,\,\,\,........\left( 1 \right)}}{{{{[\sqrt {{{\rm{I}}_1}} - \sqrt {{{\rm{I}}_2}} ]}^2} = (0.95){{\rm{I}}_{\rm{m}}}\,\,\,\,........\left( 2 \right)}}$
$ \Rightarrow \frac{{\sqrt {{I_1}} + \sqrt {{I_2}} }}{{\sqrt {{I_1}} - \sqrt {{I_2}} }} = {\left[ {\frac{{1.05}}{{0.95}}} \right]^{1/2}} = 1.05$
$\Rightarrow \frac{\sqrt{\mathrm{x}}+1}{\sqrt{\mathrm{x}}-1}=1.05 \quad\left(\mathrm{x}=\frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}\right)$
On solving
$\mathrm{x}=\frac{1681}{1}$
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