Understanding Wave Transmission
An electromagnetic wave travels from vacuum into a non-magnetic medium. We are given the incident electric field amplitude, $E_0$, and the transmitted electric field amplitude, $E_t = 2E_0/3$. We need to find the refractive index, $n$, of the medium.
Calculating Transmission Coefficient
The transmission coefficient ($t$) relates the transmitted electric field amplitude to the incident electric field amplitude:
$t = \frac{E_t}{E_0}$Substituting the given values:
$t = \frac{2E_0/3}{E_0} = \frac{2}{3}$Relating Transmission Coefficient to Refractive Index
For an electromagnetic wave normally incident from vacuum (refractive index $n_1 = 1$) onto a non-magnetic medium (refractive index $n_2 = n$), the transmission coefficient ($t$) is given by the formula:
$t = \frac{2n_1}{n_1 + n_2}$Since the wave is incident from vacuum, $n_1 = 1$. Let the refractive index of the medium be $n$. The formula becomes:
$t = \frac{2(1)}{1 + n} = \frac{2}{1 + n}$Solving for Refractive Index (n)
Now, we equate the two expressions for the transmission coefficient:
- From the given amplitudes: $t = 2/3$
- From the formula: $t = 2 / (1 + n)$
Therefore:
$\frac{2}{3} = \frac{2}{1 + n}$By comparing the denominators (since the numerators are equal):
$3 = 1 + n$Solving for $n$:
$n = 3 - 1 = 2$The refractive index of the medium is 2.
Important Questions from Reflection and Refraction
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