Two coherent sources of light interfere. The intensity ratio of two sources is $1: 4$. For this interference pattern if the value of $\frac{I_{\max }+I_{\min }}{I_{\max }-I_{\min }}$ is equal to $\frac{2 \alpha+1}{\beta+3}$, then $\frac{\alpha}{\beta}$ will be :
Solution
<p>${I_{\max }} = {\left( {\sqrt {{I_1}} + \sqrt {{I_2}} } \right)^2}$</p>
<p>${I_{\min }} = {\left( {\sqrt {{I_1}} - \sqrt {{I_2}} } \right)^2}$</p>
<p>$\therefore$ $${{{I_{\max }} + {I_{\min }}} \over {{I_{\max }} - {I_{\min }}}} = {{2({I_1} + {I_2})} \over {4 \times \sqrt {{I_1}{I_2}} }}$$</p>
<p>$$ = {1 \over 2} \times {{\left( {{{{I_1}} \over {{I_2}}} + 1} \right)} \over {\sqrt {{{{I_1}} \over {{I_2}}}} }}$$</p>
<p>$$ = {1 \over 2} \times {{\left( {{1 \over 4} + 1} \right)} \over {\left( {{1 \over 2}} \right)}}$$</p>
<p>$= {5 \over 4} = {{2 \times 2 + 1} \over {1 + 3}}$</p>
<p>$\therefore$ ${\alpha \over \beta } = {2 \over 1} = 2$</p>
About this question
Subject: Physics · Chapter: Optics · Topic: Reflection and Mirrors
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