JEE MAIN - Physics (2022 - 27th July Evening Shift - No. 14)
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 :
1.5
2
0.5
1
Explanation
$${I_{\max }} = {\left( {\sqrt {{I_1}} + \sqrt {{I_2}} } \right)^2}$$
$${I_{\min }} = {\left( {\sqrt {{I_1}} - \sqrt {{I_2}} } \right)^2}$$
$$\therefore$$ $${{{I_{\max }} + {I_{\min }}} \over {{I_{\max }} - {I_{\min }}}} = {{2({I_1} + {I_2})} \over {4 \times \sqrt {{I_1}{I_2}} }}$$
$$ = {1 \over 2} \times {{\left( {{{{I_1}} \over {{I_2}}} + 1} \right)} \over {\sqrt {{{{I_1}} \over {{I_2}}}} }}$$
$$ = {1 \over 2} \times {{\left( {{1 \over 4} + 1} \right)} \over {\left( {{1 \over 2}} \right)}}$$
$$ = {5 \over 4} = {{2 \times 2 + 1} \over {1 + 3}}$$
$$\therefore$$ $${\alpha \over \beta } = {2 \over 1} = 2$$
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