Question 185: EM waves

Question

An electromagnetic wave, whose wave normal makes an angle of $$45^{\circ}$$ with the vertical, travelling in air strikes a horizontal liquid surface. While travelling through the liquid it gets deviated through $$15^{\circ}$$. What is the speed of the electromagnetic wave in the liquid, if the speed of electromagnetic wave in air is $$3 	imes 10^8 \mathrm{~m} / \mathrm{s}$$ ? $$\left(\sin 30^{\circ}=0.5, \sin 45^{\circ}=\frac{1}{\sqrt{2}}ight)$$

Accepted Answer

The angle of incidence is $$\mathrm{i}=45^{\circ}$$
The angle of deviation is $$\delta=15^{\circ}$$
The angle of refraction is
$$\begin{aligned}
& \delta=i-r \
& r=i-\delta \
& r=45^{\circ}-15^{\circ} \
& r=30^{\circ}
\end{aligned}$$
The relation between the speed of the wave in the medium, the angle of incidence and the angle of refraction is given by the formula:
$$\begin{aligned}
& \frac{v_2}{v_1}=\frac{\sin r}{\sin i} \
& \frac{v_2}{v_1}=\frac{\sin 30^{\circ}}{\sin 45^{\circ}} \
& \frac{v_2}{v_1}=\frac{1}{\sqrt{2}}\
& \begin{aligned}
& \mathrm{v}_2=\frac{\mathrm{v}_1}{\sqrt{2}} \
& \mathrm{v}_2=\frac{3 	imes 10^8}{\sqrt{2}} \
& \mathrm{v}_2=2.1 	imes 10^8 \mathrm{~m} / \mathrm{s}
\end{aligned}
\end{aligned}$$

Answer

$$\frac{\sqrt{2}}{3} 	imes 10^8 \mathrm{~m} / \mathrm{s}$$

Answer

$$1.5 	imes 10^8 \mathrm{~m} / \mathrm{s}$$

Answer

$$2.1 	imes 10^8 \mathrm{~m} / \mathrm{s}$$

Answer

$$2.5 	imes 10^8 \mathrm{~m} / \mathrm{s}$$

EM waves

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