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An electromagnetic wave of frequency \( \nu = 3.0 \mathrm{MHz} \) passes from vacuum into a dielectric medium with relative permittivity \( \varepsilon_r = 4.0 \). Then

1. wavelength is doubled and frequency is unchanged
2. wavelength is doubled and frequency becomes half
3. wavelength is halved and frequency remains unchanged
4. wavelength and frequency both remain unchanged

Correct answer: wavelength is halved and frequency remains unchanged

Solution

When an electromagnetic wave enters a dielectric medium, its frequency remains unchanged, but its wavelength decreases by a factor of the square root of the relative permittivity. Here, the wavelength is halved because the square root of 4 is 2.

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