Find the ratio of maximum intensity to the minimum intensity in the interference pattern if the widths of the two slits in Young's experiment are in the ratio of 9 : 16. (Assuming intensity of light is directly proportional to the width of slits)

<p>Let,</p> <p>Width of first slit = w₁ and width of second slit = w₂</p> <p>Given, ${{{w_1}} \over {{w_2}}} = {9 \over {16}}$</p> <p>Given,</p> <p>Intensity of light $(I) \propto w$</p> <p>$\therefore$ ${{{I_1}} \over {{I_2}}} = {{{w_1}} \over {{w_2}}} = {9 \over {16}}$</p> <p>We know,</p> <p>$${{{I_{\max }}} \over {{I_{\min }}}} = {\left( {{{\sqrt {{I_1}} + \sqrt {{I_2}} } \over {\sqrt {{I_1}} - \sqrt {{I_2}} }}} \right)^2}$$</p> <p>$$ = {\left( {{{\sqrt {{{{I_1}} \over {{I_2}}}} + 1} \over {\sqrt {{{{I_1}} \over {{I_2}}}} - 1}}} \right)^2}$$</p> <p>$= {\left( {{{{3 \over 4} + 1} \over {{3 \over 4} - 1}}} \right)^2}$</p> <p>$= {\left( {{7 \over 1}} \right)^2}$</p> <p>$= {{49} \over 1}$</p>