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Chapter 12: Problem 93

Explain why the sky is blue and the sunset is yellow-orange.

Short Answer

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Question: Explain the concept of Rayleigh Scattering and how it affects the color of the sky during the day and sunset. Answer: Rayleigh Scattering is a phenomenon that occurs when sunlight interacts with molecules and particles in the Earth's atmosphere, causing the sunlight to scatter in all directions. The intensity of scattering is inversely proportional to the fourth power of the wavelength of the light. As per this relation, shorter wavelengths (blue, indigo, violet) are scattered more than the longer wavelengths (red, orange, yellow). During the daytime, sunlight travels through a smaller portion of the atmosphere, causing the scattered blue light to dominate over other colors, resulting in a blue sky. At sunset, sunlight travels through a larger portion of the atmosphere, scattering most of the blue light away before reaching the observer. The longer wavelengths (red, orange, and yellow) are less scattered and become more prominent, making the sky appear yellow-orange during sunset.

Step by step solution

01

Understand the sunlight composition

Sunlight is made up of a range of colors, including red, orange, yellow, green, blue, indigo, and violet. These colors form a continuous spectrum, and when combined, they produce white light. Sunlight appears white to us because it contains all these colors in almost equal intensities.
02

Introduction to Rayleigh Scattering

Rayleigh Scattering is a phenomenon that occurs when sunlight interacts with molecules and particles in the Earth's atmosphere. It causes the sunlight to scatter in all directions. The intensity of scattering is inversely proportional to the fourth power of the wavelength of the light. In mathematical terms, it is given by the relation: I ∝ (1/λ^4) Where I is the intensity of scattering and λ is the wavelength of the light.
03

Scattering of different colors of sunlight

As per the Rayleigh Scattering relation, shorter wavelengths are scattered more than the longer wavelengths. Due to this, colors like blue, indigo and violet (having shorter wavelengths) are scattered more than colors like red, orange, and yellow (having longer wavelengths). However, our eyes are more sensitive to blue rather than indigo and violet; thus, we perceive the sky as blue.
04

Color of the sky during the day

During the daytime, when sunlight travels through a smaller portion of the Earth's atmosphere, the scattered blue light dominates over the other colors due to its higher scattering intensity, resulting in the sky of a blue appearance.
05

Color of the sky during sunset

At sunset, the sunlight has to travel through a larger portion of the Earth's atmosphere. Due to the increased distance, most of the shorter wavelength blue light is scattered away before reaching the observer. The remaining colors, which have a longer wavelength (red, orange, and yellow), are less scattered and thus become more prominent. This is why the sky appears yellow-orange during sunset.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sunlight Composition
At the heart of many natural phenomena lies the composition of sunlight. It is essential to recognize that sunlight is made up of a diverse spectrum of colors. Each component of this spectrum is a color visible to the human eye—ranging from red to violet. When these colors combine, we perceive sunlight as white. This mixing of colors is the cornerstone to understanding why the sky changes color.
Consider the sunlight striking Earth's atmosphere; it's composed of these colors at different wavelengths. Red light has a longer wavelength, while blue light is at the shorter end of the visible spectrum. The distinctions in wavelengths are pivotal as they interact in varying degrees with the atmosphere, giving rise to a breathtakingly blue sky or a warmly hued sunset.
Wavelength-Dependent Scattering
Rayleigh Scattering is a fascinating phenomenon responsible for much of the color we see in the sky. At a microscopic level, when sunlight meets the molecules and minute particles in Earth's atmosphere, it doesn't just pass through; instead, it scatters in multiple directions. The degree of this scattering is heavily dependent on the light's wavelength.
A simple yet powerful relationship exists where the intensity of the light scattered, denoted as 'I', is inversely proportional to the fourth power of the wavelength (\[\begin{equation} I \propto \frac{1}{\lambda^4} \end{equation}\]). What does this mean in simpler terms? It implies that the shorter the wavelength of the light, the more intensely it gets scattered. Thus, blues and violets, with their shorter wavelengths, are scattered far more than reds and oranges.
Atmospheric Optics
To unlock the mysteries of the sky's color palette, one must delve into the study of atmospheric optics—an area exploring how light behaves as it travels through Earth's atmosphere. This field combines principles from both physics and meteorology to elucidate the interactions between light and the air above us.
Atmospheric optics doesn't just explain the scattering of light. It encompasses a wide array of captivating visual spectacles, from rainbows formed by light refraction in water droplets to the halos and glories created by light interacting with ice crystals. Each scenario is governed by the properties of light and the medium it encounters, creating an intricate dance of physics and chemistry that paints the sky.
Sky Color Explanation
Now, let's piece together the puzzle of why the sky is predominantly blue during the day and transfigures into shades of yellow to orange at sunset. During the day, sunlight has the shortest path through the atmosphere, which means that the more intensely scattered blue light dominates the sky’s appearance. This is why the clear daytime sky is blue.
As the sun sets, the light has to traverse a more extended path through the atmosphere. Most of the blue light has already been scattered out of the line of sight, leaving behind the longer wavelengths—red, orange, and yellow. These colors, now less obscured by blue, show up more prominently, and as a result, the sky near the horizon during sunset indeed appears to be painted with a palette of warm colors, creating spectacular sunsets that have captivated human gazes throughout time.

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Most popular questions from this chapter

At a wavelength of \(0.7 \mu \mathrm{m}\), the black body emissive power is equal to \(10^{8} \mathrm{~W} / \mathrm{m}^{3}\). Determine \((a)\) the temperature of the blackbody and \((b)\) the total emissive power at this temperature.

A small body is placed inside of a spherical stainless steel chamber with a diameter of \(3 \mathrm{~m}\). The chamber is evacuated and has a constant surface temperature of \(500 \mathrm{~K}\). Determine the radiation incident on the surface of the small body inside the chamber if the interior surface of the chamber is \((a)\) coated black and \((b)\) well-polished.

Define the properties reflectivity and transmissivity and discus the different forms of reflection.

A flame from a match may be approximated as a blackbody at the effective surface temperature of \(1700 \mathrm{~K}\), while moonlight may be approximated as a blackbody at the effective surface temperature of \(4000 \mathrm{~K}\), respectively. Determine the peak spectral blackbody emissive power for both lighting sources (match flame and moonlight).

Explain why surfaces usually have quite different absorptivities for solar radiation and for radiation originating from the surrounding bodies.
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