Question

An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be ________ × 10⁻² cm.

Hint:

Frequency never changes when a wave enters a different medium; only speed and wavelength change.

Answer 1

Correct Answer: 667

Step 1: Refractive index $n = \sqrt{\varepsilon_r \mu_r}$. Assuming non-magnetic medium, $n = \sqrt{2.25} = 1.5$.
Step 2: Speed in medium $v = c/n = (3 \times 10^8)/1.5 = 2 \times 10^8 \text{ m/s}$.
Step 3: Wavelength $\lambda = v/f = (2 \times 10^8)/(3 \times 10^9) = \frac{2}{30} \text{ m} = 0.0667 \text{ m}$.
Step 4: $0.0667 \text{ m} = 6.67 \text{ cm} = 667 \times 10^{-2} \text{ cm}$.