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 Question:
We need to evaluate the truthfulness of an Assertion and a Reason related to the scattering of light, and then determine if the Reason correctly explains the Assertion.
Step 2: Detailed Explanation:
Analysis of Assertion (A):
"Tiny air molecules scatter blue light more than red light." This phenomenon is known as Rayleigh scattering. According to Rayleigh's law of scattering, the intensity of scattered light (\(I_s\)) is inversely proportional to the fourth power of the wavelength (\(\lambda\)) of the light, provided the scatterer's size is much smaller than the wavelength.
\[ I_s \propto \frac{1}{\lambda^4} \] Since blue light has a shorter wavelength (\(\lambda_{blue}<\lambda_{red}\)), it is scattered much more strongly than red light by the air molecules. Thus, Assertion (A) is true.
Analysis of Reason (R):
"The refractive index of a medium is greater for blue light than red light." This phenomenon is called dispersion. According to Cauchy's relation, the refractive index (n) of a transparent medium depends on the wavelength (\(\lambda\)), approximately as \(n(\lambda) = A + \frac{B}{\lambda^2}\), where A and B are constants. Since \(\lambda_{blue}<\lambda_{red}\), the refractive index for blue light (\(n_{blue}\)) is greater than for red light (\(n_{red}\)). Thus, Reason (R) is true.
Relating Reason and Assertion:
The scattering of light by molecules is due to the absorption and re-radiation of light by the electrons in the molecules. The molecules behave like oscillating dipoles under the influence of the light's electric field. The polarizability of the molecules, which determines how strongly they interact with light, is related to the refractive index of the medium. A higher refractive index (as for blue light) implies a stronger interaction between light and the medium, leading to more scattering. Therefore, the fact that the refractive index is wavelength-dependent is the underlying physical cause for Rayleigh scattering. Hence, (R) is the correct explanation for (A).
Step 3: Final Answer:
Both Assertion (A) and Reason (R) are true statements, and the Reason provides the correct physical explanation for the Assertion.