A : When a light wave travels from a rarer to a denser medium, it looses speed. The reduction in speed imply a reduction in energy carried by the light wave.
R : The energy of a wave of proportional to frequency of wave.

Options

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

Answer

To solve the problem, we need to analyze the two statements given:

**Assertion (A):** When a light wave travels from a rarer to a denser medium, it loses speed. The reduction in speed implies a reduction in energy carried by the light wave.
**Reason (R):** The energy of a wave is proportional to the frequency of the wave.

### Step-by-Step Solution:

1. **Analyze the Assertion (A):**
- When light travels from a rarer medium (like air) to a denser medium (like water or glass), it indeed loses speed. This part of the assertion is true.
- However, the second part of the assertion states that this reduction in speed implies a reduction in energy carried by the light wave. This is incorrect. The energy of a light wave is not solely dependent on its speed but rather on its amplitude and frequency.

2. **Analyze the Reason (R):**
- The reason states that the energy of a wave is proportional to its frequency. This statement is partially true, as the energy of a photon (quantum of light) is indeed proportional to its frequency (E = hf, where h is Planck's constant). However, this does not apply to classical wave energy in the same way, as wave energy is more directly related to the square of the amplitude.
- Therefore, while the frequency remains constant when light moves from one medium to another, the energy of the wave is not solely dependent on frequency in the context of classical wave behavior.

3. **Conclusion:**
- Since the assertion is partially true (the first part is true, but the second part is false), and the reason is also partially true (it is true in the context of photons but misleading in the context of classical waves), we conclude that both statements cannot be considered entirely true.
- Therefore, both the assertion and the reason are false in the context provided.

### Final Answer:
Both the assertion and the reason are false.