Question

Just after sunrise, you look north at the sky just above the horizon. Is the light you see polarized? If so, in what direction?

Short answer

Answer: Yes, the light from the sky just above the horizon just after sunrise is polarized. It is polarized in the horizontal direction.

Step-by-step solution

Understanding the scattering of sunlight and polarization

Sunlight consists of unpolarized light. When it enters the Earth's atmosphere, it gets scattered by the air molecules, dust and aerosols particles. This process of scattering is highly dependent on the angle between the incident sunlight and the direction in which the scattered light is observed. The phenomenon responsible for the polarization of scattered light is known as Rayleigh scattering.

Principle of Rayleigh scattering and Brewster's angle

Rayleigh scattering asserts that the degree of polarization of scattered light depends on the angle between the incident light (sunlight) and the observer (us). At a specific angle, called the Brewster's angle, the degree of polarization is maximum, and the scattered light becomes completely polarized. Brewster's angle is given by the formula \(\theta_B = \cot^{-1} \left( \frac{n_2}{n_1} \right)\), where \(n_1\) and \(n_2\) are the refractive indices of the two media involved.

Determining the position of the sun and observer

Just after sunrise, the sun is approximately at the horizon in the east direction. When we look north, we are looking perpendicular to the direction of sunlight. So, the angle between the incident sunlight and the observer's direction is 90 degrees.

Evaluating the polarization in the given scenario

Since the angle between the incident sunlight and the observer's direction is 90 degrees, and considering that a 90-degree angle is a typical Brewster's angle in air, we can conclude that the light from the sky just above the horizon is polarized.

Finding the direction of polarization

The direction of polarization is perpendicular to the plane containing the incident light and the scattered light. In this case, since we are looking north and the sunlight is coming from the east, the plane containing the incident light and the scattered light will be a vertical plane. Therefore, the direction of polarization will be horizontal. In conclusion, the light from the sky just above the horizon, just after sunrise, is polarized in the horizontal direction.