Question

Young's expt. the ratio of intensity at maxima and minima in the interference pattern is The 25 : 9. The ratio of slit width will be

• A. 4 : 1
• B. 2 : 1
• C. 16 : 1
• D. 8 : 1

Answer 1

The correct option is C 16 : 1

$\frac{I_{max}}{I_{min}}=\left(\frac{25}{9}\right)=\left(\frac{a_1+a_2}{a_1-a_2}\right)$
$\frac{5}{3}=\left(\frac{a_1+a_2}{a_1-a_2}\right)$
$5a_1-5a_2=3a_1+3a_2$
$2a_1=8a_2$
$\frac{a_1}{a_2}=4$
$\frac{a_1}{a_2}=\sqrt{\frac{{\omega }_1}{{\omega }_2}}=\frac{4}{1}$
$\left(\frac{{\omega }_1}{{\omega }_2}\right)=\frac{16}{1}$