Question

Two light waves of intensities ${}^{\prime }{I}_1^{\prime }$ and ${}^{\prime }{I}_2^{\prime }$ having same frequency pass through same medium at a time in same direction and interfere. The sum of the minimum and maximum intensities is

• A. $(I_1+I_2)$
• B. $2(I_1+I_2)$
• C. $(\sqrt{I_1}+\sqrt{I_2})$
• D. $(\sqrt{I_1}-\sqrt{I_2})$

Answer 1

Answer: (B)

We know that,
$I_{\max }={\left(a_1+a_2\right)}^2...(i)$
$I_{\min }={\left(a_1-a_2\right)}^2...(ii)$
On adding Eqs. (i) and (ii), we get
$I_{\max }+I_{\min }={\left(a_1+a_2\right)}^2+{\left(a_1-a_2\right)}^2$
$I_{\max }+I_{\min }=a_1^2+a_2^2+2a_1{a}_2+a_1^2+a_2^2-2a_1{a}_2$
$I_{\max }+I_{\min }=2\left(a_1^2+a_2^2\right)$
But $l\propto a^2$
Therefore, $I_{\max }+I_{\min }=2(I_1+I_2)$