QJEEM22Phf5b0: JEE Main 2022 Physics - Class 12 JEEM22Phf5b0 Solution: Two coherent sources of light interfere. The intensity ratio of …

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

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

$\therefore$ ${{{I_{\max }} + {I_{\min }}} \over {{I_{\max }} - {I_{\min }}}} = {{2({I_1} + {I_2})} \over {4 \times \sqrt {{I_1}{I_2}} }}$

$= {1 \over 2} \times {{\left( {{{{I_1}} \over {{I_2}}} + 1} \right)} \over {\sqrt {{{{I_1}} \over {{I_2}}}} }}$

$= {1 \over 2} \times {{\left( {{1 \over 4} + 1} \right)} \over {\left( {{1 \over 2}} \right)}}$

$= {5 \over 4} = {{2 \times 2 + 1} \over {1 + 3}}$

$\therefore$ ${\alpha \over \beta } = {2 \over 1} = 2$