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The electric field of an electromagnetic wave travelling through a medimn is given by $$\overrightarrow{E}(x,t)=25\sin(2.0\times 10^{15}t-10^{7}x)\widehat{n}$$ then the refractive index of the medium is______.
(All given measurement are in SI uits)
We need to find the refractive index of the medium.
$$E = 25\sin(2.0 \times 10^{15}t - 10^7 x)$$
$$\omega = 2.0 \times 10^{15}$$ rad/s, $$k = 10^7$$ rad/m
Speed of wave in medium:
$$v = \frac{\omega}{k} = \frac{2 \times 10^{15}}{10^7} = 2 \times 10^8$$ m/s
Refractive index:
$$n = \frac{c}{v} = \frac{3 \times 10^8}{2 \times 10^8} = 1.5$$
Therefore, the refractive index is Option 1: 1.5.
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