A : All electromagnetic waves travel through vacuum with same speed by they have different wavelength or frequency.
R : The wavelength of the electromagnetic waves is often correlated with and characteristic size of the system that produces and radiates them.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To analyze the statements provided in the question, we will break down both the assertion (A) and the reason (R) step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that all electromagnetic (EM) waves travel through a vacuum at the same speed, but they have different wavelengths and frequencies.
- This is true because the speed of light in a vacuum is a constant value, approximately \(3 \times 10^8\) meters per second.

2. **Understanding the Relationship Between Wavelength and Frequency**:
- The relationship between the speed of light (c), wavelength (λ), and frequency (f) is given by the equation:
\[ c = f \times \lambda \]
- Since the speed of light (c) is constant in a vacuum, if the frequency (f) changes, the wavelength (λ) must also change to maintain this equation.

3. **Understanding the Reason (R)**:
- The reason states that the wavelength of electromagnetic waves is often correlated with the characteristic size of the system that produces and radiates them.
- This means that different sources of EM waves (like X-rays, gamma rays, or UV rays) have different characteristic sizes, which influence the frequency and thus the wavelength of the waves they emit.

4. **Connecting Assertion and Reason**:
- The assertion is correct because all EM waves travel at the same speed in a vacuum, but they can have different wavelengths and frequencies depending on the source.
- The reason is also correct as it explains why different sources produce EM waves of different wavelengths, correlating with their characteristic sizes.

5. **Conclusion**:
- Since both the assertion (A) and reason (R) are true, and the reason correctly explains the assertion, we can conclude that the answer is that both statements are correct, and the reason supports the assertion.

### Final Answer:
Both A and R are true, and R is the correct explanation of A.

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