Dispersion and polarization of light

Solution:

Decomposition of Light

White light is a mixture of seven monochromatic colors (red, orange, yellow, green, blue, indigo, violet), i.e., a mixture of electromagnetic waves with different frequencies.

Individual colored lights propagate in a medium at different speeds $v < c$,
therefore they have different refractive indices and refract at different angles.

$$n = \frac{\lambda_0}{\lambda} = \frac{c}{\frac{c}{\lambda f}} = \frac{c}{\lambda f}$$ $$v = \frac{c}{n} = \frac{c}{\frac{c}{\lambda f}} = \lambda f$$

Polarization of Light

Natural light is unpolarized. It is a transverse electromagnetic wave, characterized by oscillations of mutually perpendicular vectors
$\vec{E}\perp \vec{B}$. On the retina of the eye, only the oscillations of the vector of electric field intensity $\vec{E}$ act.
In polarized light, the oscillation of vector $\vec{E}$ occurs in one plane.

Complete polarization occurs when the angle of incidence is the so-called Brewster’s angle $\alpha_p$.

$$\tan \alpha_p = \frac{n_2}{n_1}$$

At the polarization angle $\alpha_p$, the reflected ray is perpendicular to the refracted ray.

Solution:

Analysis:

The wavelength of the hydrogen line H₂ in water is λ = 493.5nm.

Solution:

a) In vacuum:

$$n = \frac{c}{v}$$$$$$

$$v = \frac{c}{n} = \frac{c}{1} = c$$$$$$

$$v = c \;-\; \text{does not depend on frequenc$$

b) In a medium:

$$n = \frac{c}{v}$$$$$$

$$v = \frac{c}{n} = \frac{c}{f\lambda} = f\lambda$$$$$$

$$v = f\lambda \;-\; \text{depends on frequenc$$ 

In vacuum, the speed of light does not depend on frequency, in a medium it does.