Question 67: Wave Optics

Question

Two plane polarized light waves combine at a certain point whose electric field components are
$\begin{aligned}
& E_1=E_0 \operatorname{Sin} \omega t \
& E_2=E_0 \operatorname{Sin}\left(\omega t+\frac{\pi}{3}ight)
\end{aligned}$
Find the amplitude of the resultant wave.

Accepted Answer

To find the amplitude of the resultant wave for the given electric field components, we use the formula for the resultant amplitude of two combining waves. These components are:
$ E_1 = E_0 \sin \omega t $
$ E_2 = E_0 \sin \left(\omega t + \frac{\pi}{3}\right) $
The general formula for the amplitude $ E $ of two superimposed waves $ E_1 $ and $ E_2 $ with a phase difference is:
$ E = \sqrt{E_1^2 + E_2^2 + 2E_1E_2 \cos\phi} $
where $ \phi $ is the phase difference between the two waves. In this scenario, $ \phi = \frac{\pi}{3} $.
Substituting the given expressions and phase difference into the formula, we get:
$ E = \sqrt{(E_0)^2 + (E_0)^2 + 2(E_0)(E_0)\cos\left(\frac{\pi}{3}\right)} $
Given that $\cos \left( \frac{\pi}{3} \right) = \frac{1}{2}$, this simplifies to:
$ E = \sqrt{2E_0^2 + E_0^2} = \sqrt{3}E_0 $
Thus, the amplitude of the resultant wave is $\sqrt{3}E_0 \approx 1.73E_0$.

Answer

$1.7 \mathrm{~E}_0$

Answer

$\mathrm{E}_0$

Answer

$0.9 \mathrm{~E}_0$

Answer

$3.4 \mathrm{~E}_0$

Wave Optics

Two plane polarized light waves combine at a certain point whose electric field components are \begin{aligned} & E_1=E_0 \operatorname{Sin} \omega t \\ & E_2=E_0 \operatorname{Sin}\left(\omega t+\frac{\pi}{3}\right) \end{aligned} Find the amplitude of the resultant wave.

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