15. Two slits in Young’s experiment have widths in the ratio 1 : 25. The ratio of intensity at the maxima and minima in the interference pattern, $I_{max}$⁄$I_{min}$ is :

15. Two slits in Young’s experiment have widths in the ratio 1 : 25. The ratio of intensity at the maxima and minima in the interference pattern, I_max/I_min is :

\( (a)\; \tfrac{121}{49} \)  

\( (b)\; \tfrac{49}{121} \)  

\( (c)\; \tfrac{4}{9} \)  

\( (d)\; \tfrac{9}{4} \)  

Answer :  \( (d)\; \tfrac{9}{4} \)  

\( \frac{W_1}{W_2} = \frac{I_1}{I_2} = \frac{1}{25} \)

\(  \frac {I_{\text{max}}}{I_{\text{min}}}= \left( \frac{\sqrt{I_1} + \sqrt{I_2}}{\sqrt{I_1} - \sqrt{I_2}} \right)^2 \)

\( = \left( \frac{1 + 5}{1 - 5} \right)^2 \)

\( = \left( \frac{6}{-4} \right)^2 \)

\( = \left( \frac{3}{2} \right)^2 \)

\( = \frac{9}{4} \)