Question

Assertion (A): Tiny air molecules scatter blue light more than red light.
Reason (R): The refractive index of a medium is greater for blue light than red light.

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

Hint:

Remember Rayleigh scattering: \(I \propto 1/\lambda^4\). Shorter wavelength (blue/violet) scatters most, which is why the sky is blue. Longer wavelength (red/orange) scatters least, which is why sunsets are red.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Rayleigh scattering explains why the sky is blue, while the refractive index explains how light bends in a medium.
Step 2: Detailed Explanation:
Assertion (A): Rayleigh's Law of Scattering states that the intensity of scattered light is inversely proportional to the fourth power of the wavelength (\( I \propto 1/\lambda^4 \)). Since blue light has a shorter wavelength than red light, it is scattered more. (A is true).
Reason (R): Cauchy's formula states that refractive index \( \mu \) increases as wavelength decreases. Thus, \( \mu_{blue}>\mu_{red} \). (R is true).
However, scattering is caused by the interaction of light with particles much smaller than its wavelength, whereas refractive index describes the phase velocity of light in a bulk medium. The reason for scattering is the small wavelength, not the high refractive index.
Step 3: Final Answer:
Both statements are correct, but R does not explain why A happens.