Propagation In A Medium

Inside a material medium an electromagnetic wave slows because the medium's permittivity and permeability replace those of free space, giving v = \frac{1}{\sqrt{\mu \varepsilon}} = \frac{c}{\sqrt{\mu_r \varepsilon_r}}. With \varepsilon_r = 4 and \mu_r = 1, the denominator becomes \sqrt{4 \times 1} = 2, so v = (3.0 \times 10^{8})/2 = 1.5 \times 10^{8}\ \text{m/s}. The 3.0 \times 10^{8}\ \text{m/s} option ignores the medium and quotes the vacuum speed. The 0.75 \times 10^{8}\ \text{m/s} value wrongly divides by \varepsilon_r itself rather than its square root, giving a factor of four. The 6.0 \times 10^{8}\ \text{m/s} option, faster than light, is unphysical and would require multiplying instead of dividing. The effective refractive index here is n = \sqrt{\mu_r \varepsilon_r} = 2, exactly the factor by which the speed drops, in line with the NCERT and JEE treatment linking optics to electromagnetism. While the wave slows, its frequency stays fixed by the source, so it is the wavelength inside the medium that shrinks by the same factor of two. This reduction in wavelength while frequency is preserved is the microscopic origin of refraction observed in ordinary optics. As a plausibility check, any genuine medium must give a speed below c, and 1.5 \times 10^{8}\ \text{m/s} satisfies that requirement.