Question

How does refractive index of any medium depend upon the wavelength of light?

Hint:

Refractive index (\(n\)) decreases with increasing wavelength (\(\lambda\)) in most media. Shorter wavelengths (blue/violet) bend more than longer wavelengths (red).

Answer 1

The refractive index (\(n\)) of a medium is a measure of how much the speed of light is reduced inside that medium compared to the speed of light in a vacuum. It is given by the equation: \[ n = \frac{c}{v} \] Where: - \(c\) is the speed of light in vacuum (\(3 \times 10^8 \, \text{m/s}\)), - \(v\) is the speed of light in the medium. The refractive index is \textit{not constant} for all wavelengths of light. It depends on the wavelength of the light passing through the medium, a phenomenon known as dispersion. Typically, the refractive index decreases as the wavelength of light increases, which is why shorter wavelengths (like violet light) bend more than longer wavelengths (like red light) when passing through a prism or any refractive medium.
The relationship between refractive index and wavelength can be described as follows: - For shorter wavelengths (like blue or violet light), the refractive index is higher. This is because the interaction between light and the particles in the medium causes more bending of shorter wavelengths. - For longer wavelengths (like red light), the refractive index is lower, and the light bends less.
Thus, the refractive index (\(n\)) is inversely related to the wavelength of light (\(\lambda\)) in most materials. This is summarized in the equation for dispersion: \[ n(\lambda) = n_0 \left(1 + \frac{A}{\lambda^2}\right) \] Where \(n_0\) is the refractive index at a reference wavelength, and \(A\) is a constant that depends on the material.
In summary, as the wavelength of light increases, the refractive index generally decreases, which results in less bending of longer wavelengths in the medium.