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Wave Optics — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsWave Optics3 Marks
Question
Two monochromatic light waves of equal intensities produce an interference pattern. At a point in the pattern, the phase difference between the interfering waves is $\pi / 3 rad$. Express the intensity at this point as a fraction of the maximum intensity in the pattern.
✓

Answer

Data $: I_1=I_2=I_{\square}, \varphi=\pi / 3 rad$
The resultant intensity at the point in the pattern is
$
\begin{aligned}
I & =I_{\max } \cos ^2 \frac{\phi}{2} \text { } \\
& =I_{\max }\left(\cos \frac{\pi}{6}\right)^2=I_{\max }\left(\frac{\sqrt{3}}{2}\right)^2 \\
\therefore I & =\frac{3}{4} I_{\max }
\end{aligned}
$

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