First slide

Electromagnetic waves and its nature

Question

If the wave front of electromagnetic wave travelling in vacuum is given by $\vec{r} = \hat{i} + \hat{j} + \hat{k}$ , find the angle made by the direction of propagation of electromagnetic wave with z-axis?

Moderate

A

$θ = \cos^{- 1} (\frac{1}{3})$
B

$θ = \cos^{- 1} (\frac{2}{3})$
C

$θ = \cos^{- 1} (\frac{1}{\sqrt{3}})$
D

$θ = \cos^{- 1} (\frac{2}{\sqrt{3}})$

Solution

If $θ$ is the angle which the direction of propagation of electro magnetic wave makes with z-axis then $\cos θ = \frac{\vec{r} . \hat{k}}{| \bar{r} |} = \frac{(\hat{i} + \hat{j} + \hat{k}) . \hat{k}}{\sqrt{{(1)}^{2} + {(1)}^{2} + {(1)}^{2}}} = \frac{1}{\sqrt{3}} \Rightarrow θ = \cos^{- 1} (\frac{1}{\sqrt{3}})$

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