Question

Statement I: In Young's experiment, for two coherent sources, the resultant intensity is given by $I=4I_0{\cos }^2\frac{\varphi }{2}$.
Statement II: Ratio of maximum to minimum intensity
is $\frac{I_{\max }}{I_{\min }}=\frac{{\left(\sqrt{I_1}+\sqrt{I_2}\right)}^2}{{\left(\sqrt{I_1}-\sqrt{I_2}\right)}^2}$

• A. If both statements are true and statement II is the correct explanation of statement I.
• B. If both statements are true but statement II is not the correct explanation of statement I.
• C. If statement I is true but statement II is false.
• D. If both statements are false.

Answer 1

Answer: (B)

For two coherent sources,
$I=I_1+I_2+\sqrt{I_1{I}_2}\cos \theta$
Putting, $I_1=I_2=I_0$
We have $I=I_0+I_0+2\sqrt{I_0\times I_0}\cos \varphi$
Simplifying the above expression
$I=2I_0(1+\cos \varphi )$
$=2I_0\left(1+2{\cos }^2\frac{\varphi }{2}-1\right)$
$=2I_0\times 2{\cos }^2\frac{\varphi }{2}=4I_0{\cos }^2\frac{\varphi }{2}$
Also, $I_{\max }={\left(\sqrt{I_1}+\sqrt{I_2}\right)}^2$
$I_{\min }=\left(\sqrt{I_1}+\sqrt{I_2}\right)$
$\therefore \frac{I_{\max }}{I_{\min }}=\frac{{\left(\sqrt{I_1}+\sqrt{I_2}\right)}^2}{{\left(\sqrt{I_1}-\sqrt{I_2}\right)}^2}$