Question

Ratio of maximum to minimum intensity is 25:16.Calculate ratio of intensities:-

• A. 5:4
• B. 4:5
• C. 9:1
• D. 81:1

Answer 1

The correct option is D 81:1

Ratio of maximum to minimum intensity $=25:16$

ratio of intensities $=$

$\frac{I_1}{I_2}={\left(\frac{a_1}{a_2}\right)}^2=?$

$\frac{I_{max}}{I_{min}}=\frac{{(a_1+a_2)}^2}{{(a_1-a_2)}^2}$

$\frac{I_{max}}{I_{min}}=\frac{25}{16}$

$a_1+a_2=5$

$\underset{–}{a_1-a_2=4}$

${2a}_1=9$

or, $a_1=9/2$

$a_2=5-9/2=\frac{10-9}{2}=\frac{1}{2}$

$\frac{I_1}{I_2}=\frac{{\left(9/2\right)}^2}{{\left(1/2\right)}^2}=\frac{81}{4}\times 4=81:1$