Question

Two light waves of intensities $'I_1'$ and $'I_2'$ 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)

$2 (I_1 + I_2)$

Answer 2

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
$I_{\max }+I_{\min }=\left(a_{1}+a_{2}\right)^{2}+\left(a_{1}-a_{2}\right)^{2}$
$I_{\max }+I_{\min }=a_{1}^{2}+a_{2}^{2}+2 a_{1} a_{2}+a_{1}^{2}+a_{2}^{2}-2 a_{1} a_{2}$
$I_{\max }+I_{\min }=2\left(a_{1}^{2}+a_{2}^{2}\right)$
But $\,\,\,\,\, l \propto a^{2}$
Therefore, $I_{\max }+I_{\min }=2( I_{1}+I_{2})$