The electric field of an electromagnetic wave travelling through a medium is given by Then the refractive index of the medium [2026]

Question

The electric field of an electromagnetic wave travelling through a medium is given by $\vec{E} (x, t) = 25 \sin (2.0 \times 10^{15} t - 10^{7} x) \hat{n} .$ Then the refractive index of the medium is _____

(All given measurement are in SI units.) [2026]

Smart Achievers · Accepted Answer

(1)

$ω = 2 \times 10^{15} rad/s$

$k = 10^{7} m^{- 1}$

$v = \frac{2 π}{k} \cdot \frac{ω}{2 π} = \frac{ω}{k} = \frac{2 \times 10^{15}}{10^{7}} = 2 \times 10^{8} = \frac{c}{1.5}$

$\Rightarrow μ = 1.5$

Solution

Q.
The electric field of an electromagnetic wave travelling through a medium is given by $\vec{E} (x, t) = 25 \sin (2.0 \times 10^{15} t - 10^{7} x) \hat{n} .$ Then the refractive index of the medium is _____

(All given measurement are in SI units.) [2026]

1 1.5

2 1.7

3 2

4 1.2

Ans.
(1)

$ω = 2 \times 10^{15} rad/s$

$k = 10^{7} m^{- 1}$

$v = \frac{2 π}{k} \cdot \frac{ω}{2 π} = \frac{ω}{k} = \frac{2 \times 10^{15}}{10^{7}} = 2 \times 10^{8} = \frac{c}{1.5}$

$\Rightarrow μ = 1.5$

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