Question

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Rayleigh scattering causes the sky to appear blue.
Reason R: As most of the Rayleigh scatterers have size $<<$ $\lambda$ (wavelength).
In light of the above statements, choose the correct answer from the options given below:

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is NOT the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Hint:

Remember the three types of atmospheric scattering:
- Rayleigh scattering: Particle size \( \ll \lambda \) (causes blue sky).
- Mie scattering: Particle size \( \approx \lambda \) (causes white clouds due to dust/water droplets).
- Non-selective scattering: Particle size \( \gg \lambda \) (causes white fog).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Scattering is the physical process where particles suspended in a medium diffuse or redirect incoming electromagnetic radiation.
The type and intensity of scattering depend on the ratio of the scattering particle's size to the wavelength of the incident light.

Step 2: Detailed Explanation:
Let us analyze both statements and their scientific relationship:
- Reason R: Rayleigh scattering occurs when the diameter of the scattering particles (such as nitrogen and oxygen molecules in the atmosphere) is much smaller than the wavelength (\( \lambda \)) of the incident solar radiation:
\[ d \ll \lambda \]
Therefore, Reason R is true.
- Assertion A: Under this condition, the intensity of the scattered light (\( I \)) is inversely proportional to the fourth power of its wavelength:
\[ I \propto \frac{1}{\lambda^4} \]
This relationship means that shorter wavelengths of light are scattered much more effectively than longer wavelengths.
In the visible light spectrum, blue light has a much shorter wavelength (approximately \( 400 \text{ to } 450 \text{ nm} \)) than red light (approximately \( 650 \text{ to } 700 \text{ nm} \)).
Because of this difference, blue light is scattered in all directions by atmospheric gas molecules about ten times more than red light.
When we look at the sky, we see this scattered blue light, which makes the sky appear blue.
This explains how the small size of the scatterers (Reason R) leads to the Rayleigh scattering that makes the sky appear blue (Assertion A).
Therefore, both A and R are true and R is the correct explanation of A.

Step 3: Final Answer:
Both A and R are true and R is the correct explanation of A.