A: When light travels from a rarer to a denser medium, it loses some speed but it doesn't imply a reduction in the energy carried by the light wave.
R: Energy carried by a wave depends on the amplitude of the wave and not on the speed of wave propagation.

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 need to evaluate both the assertion (A) and the reason (R) given.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that when light travels from a rarer medium (like air) to a denser medium (like glass), it loses some speed. This is true because the speed of light is affected by the medium it travels through. In a denser medium, light travels slower due to the interaction with the medium's particles.

2. **Energy of Light Waves**:
- The assertion further claims that this reduction in speed does not imply a reduction in the energy carried by the light wave. The energy carried by a light wave is given by the equation:
\[ E = h \cdot \nu \]
where \(E\) is energy, \(h\) is Planck's constant, and \(\nu\) (nu) is the frequency of the light wave.

3. **Frequency and Speed Relationship**:
- When light enters a denser medium, its frequency (\(\nu\)) remains constant because it is determined by the source of the light. The speed of light decreases, but the frequency does not change. Therefore, since the energy depends on frequency, the energy remains constant.

4. **Conclusion about Assertion (A)**:
- Since the energy remains constant despite the change in speed, the assertion (A) is true.

5. **Understanding the Reason (R)**:
- The reason states that the energy carried by a wave depends on the amplitude of the wave. This statement is incorrect for light waves. The energy of a light wave does not depend on its amplitude; it depends solely on its frequency.

6. **Conclusion about Reason (R)**:
- Since the reason (R) is incorrect, we conclude that while the assertion (A) is true, the reason (R) is false.

7. **Final Evaluation**:
- Therefore, the final conclusion is that the assertion is true, but the reason is false. The correct answer to the question is that option 3 is the answer.