WBJEE · Physics · Electromagnetic Waves
The electric field of a plane electromagnetic wave in a medium is given by \(\vec{E}(x, y, z, t)=E_0 \hat{n} e^{i k_0[(x+y+z)-c t]}\) where \(c\) is the speed of light in free space. \(\vec{E}\) field is polarized in the \(x-z\) plane. The speed of wave is \(v\) in the medium. Then
- A \(\hat{\mathrm{n}}=\hat{\mathrm{i}}-\hat{\mathrm{k}} ; v=\mathrm{c}\).
- B \(\hat{\mathrm{n}}=\frac{\hat{\mathrm{i}}-\hat{\mathrm{k}}}{\sqrt{2}} ; v=\frac{\mathrm{c}}{\sqrt{3}}\)
- C refractive index of the medium is \(\sqrt{3}\)
- D \(\hat{n}=\frac{\hat{\mathrm{i}}+\hat{\mathrm{k}}}{\sqrt{2}} ; v=\frac{\mathrm{c}}{\sqrt{2}}\)
Answer & Solution
Correct Answer
(C) refractive index of the medium is \(\sqrt{3}\)
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Detailed explanation
\begin{aligned} & \text { Hint : } \overrightarrow{\mathrm{E}}=\mathrm{E}_0 \hat{n} e^{i k_0(\hat{\mathrm{k}} \cdot \hat{\mathrm{r}}-\mathrm{wt})} \\ & \Rightarrow \overrightarrow{\mathrm{k}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}} \\ & \Rightarrow…
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