Correct Option: (C) wavelength is halved and frequency remains unchanged.
Step 1 (Formula / Governing Law & Given Data): [1/3 Mark]
The speed of an electromagnetic wave in a medium is given by $v = \frac{1}{\sqrt{\mu \epsilon}}$, where $\mu = \mu_0 \mu_r$ and $\epsilon = \epsilon_0 \epsilon_r$. The refractive index $n$ of the medium is defined as:
$$n = \frac{c}{v} = \sqrt{\mu_r \epsilon_r}$$Given: Relative permittivity $\epsilon_r = \frac{3}{2}$ and relative permeability $\mu_r = \frac{8}{3}$.
Step 2 (Step-by-Step Mathematical Working): [1/3 Mark]
Calculate the refractive index $n$:
$$n = \sqrt{\left(\frac{8}{3}\right) \times \left(\frac{3}{2}\right)} = \sqrt{4} = 2$$Since the frequency $f$ of an electromagnetic wave depends only on the source, it remains unchanged when entering a new medium. The relationship between wavelength in vacuum ($\lambda_0$) and wavelength in the medium ($\lambda$) is:
$$\lambda = \frac{\lambda_0}{n} = \frac{\lambda_0}{2}$$Step 3 (Final Concluded Answer): [1/3 Mark]
As the refractive index is $2$, the wavelength becomes half of its original value in vacuum, while the frequency remains constant. Thus, the correct option is (C).
💡 EL10 Concept Insight: Think of the wave like a car driving from a smooth road onto thick mud; the car slows down (wavelength shortens), but the engine's rhythm (frequency) stays exactly the same because it's controlled by the driver (the source).