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The Human Eye and Optical Phenomena - SC ATTERING OF LIGHT

Grade 10CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Scattering of light is the phenomenon where light rays are deviated from their straight path, in all directions, after striking an obstacle like dust or gas molecules.

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Tyndall Effect: The scattering of a beam of light by colloidal particles or very fine particles in a suspension. This makes the path of light visible, such as sunlight entering a dusty room or passing through a forest canopy.

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Rayleigh Scattering Law: The intensity of scattered light is inversely proportional to the fourth power of its wavelength, provided the scattering particles are smaller than the wavelength of light. This is expressed as I∝1λ4I \propto \frac{1}{\lambda^4}.

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Color of the Sky: The molecules of air and other fine particles in the atmosphere have a size smaller than the wavelength of visible light. These are more effective in scattering light of shorter wavelengths (blue end) than light of longer wavelengths (red end). Since λblue<λred\lambda_{blue} < \lambda_{red}, blue light is scattered more, making the sky appear blue.

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Color of the Sun at Sunrise and Sunset: Light from the Sun near the horizon passes through thicker layers of air and a larger distance in the earth's atmosphere. Most of the shorter wavelengths (blue/violet) are scattered away, and only the longer wavelengths (red) reach our eyes.

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Sun at Noon: The Sun appears white at noon because the light has to travel a relatively shorter distance through the atmosphere, and only a little of the blue and violet colors are scattered.

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Danger Signals: Danger signals are red because red light has the longest wavelength in the visible spectrum. It is scattered the least by fog or smoke, allowing it to be seen from a long distance.

📐Formulae

I∝1λ4I \propto \frac{1}{\lambda^4}

λred≈1.8×λblue\lambda_{red} \approx 1.8 \times \lambda_{blue}

Scattering∝1Wavelength4\text{Scattering} \propto \frac{1}{\text{Wavelength}^4}

💡Examples

Problem 1:

Why does the sky appear dark (black) to an astronaut instead of blue?

Solution:

The sky appears dark to an astronaut because there is no atmosphere in outer space to scatter sunlight. Without atmospheric particles like oxygen and nitrogen molecules, the scattering of light (Tyndall effect or Rayleigh scattering) does not occur, and hence no light reaches the observer's eyes from the 'sky'.

Explanation:

Scattering requires a medium with particles. In a vacuum, light travels in a straight line without being deviated towards the observer's eyes from different directions.

Problem 2:

Compare the scattering of blue light (450 nm450\text{ nm}) and red light (700 nm700\text{ nm}) based on Rayleigh's law.

Solution:

According to Rayleigh's law, scattering intensity II is inversely proportional to λ4\lambda^4. Since λred>λblue\lambda_{red} > \lambda_{blue}, we can see that: IblueIred=(λredλblue)4\frac{I_{blue}}{I_{red}} = \left( \frac{\lambda_{red}}{\lambda_{blue}} \right)^4 Substituting values: IblueIred=(700450)4≈(1.55)4≈5.8\frac{I_{blue}}{I_{red}} = \left( \frac{700}{450} \right)^4 \approx (1.55)^4 \approx 5.8

Explanation:

This shows that blue light is scattered approximately 5.85.8 times more strongly than red light, which is why the blue color dominates the clear daytime sky.