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Chapter 22: Problem 53

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

Expert verified
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

01

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.
02

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.
03

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.
04

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.
05

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.

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Most popular questions from this chapter

Unpolarized light passes through two polarizers in turn with polarization axes at \(45^{\circ}\) to one another.What is the fraction of the incident light intensity that is transmitted?

The intensity of the sunlight that reaches Earth's upper atmosphere is approximately \(1400 \mathrm{W} / \mathrm{m}^{2} .\) (a) What is the average energy density? (b) Find the rms values of the electric and magnetic fields.
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The solar panels on the roof of a house measure \(4.0 \mathrm{m}\) by $6.0 \mathrm{m} .\( Assume they convert \)12 \%$ of the incident EM wave's energy to electric energy. (a) What average power do the panels supply when the incident intensity is \(1.0 \mathrm{kW} / \mathrm{m}^{2}\) and the panels are perpendicular to the incident light? (b) What average power do the panels supply when the incident intensity is \(0.80 \mathrm{kW} / \mathrm{m}^{2}\) and the light is incident at an angle of \(60.0^{\circ}\) from the normal? (W) tutorial: solar collector) (c) Take the average daytime power requirement of a house to be about 2 kW. How do your answers to (a) and (b) compare? What are the implications for the use of solar panels?
What must be the relative speed between source and receiver if the wavelength of an EM wave as measured by the receiver is twice the wavelength as measured by the source? Are source and observer moving closer together or farther apart?
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