KCET · Physics · Wave Optics
Two monochromatic light waves of amplitudes \(3 \mathrm{~A}\) and \(2 \mathrm{~A}\) interfering at a point have a phase difference of \(60^{\circ}\). The intensity at that point will be proportional to
- A \(5 A^{2}\)
- B \(13 A^{2}\)
- C \(7 A^{2}\)
- D \(19 A^{2}\)
Answer & Solution
Correct Answer
(D) \(19 A^{2}\)
Step-by-step Solution
Detailed explanation
Here, \(A=\sqrt{A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos \theta}\)
\[
\begin{gathered}
I=9 A^{2}+4 A^{2}+2 \times 3 A \times 2 A \times \frac{1}{2} \\
I=19 A^{2}
\end{gathered}
\]
\[
\begin{gathered}
I=9 A^{2}+4 A^{2}+2 \times 3 A \times 2 A \times \frac{1}{2} \\
I=19 A^{2}
\end{gathered}
\]
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