Statement-I : Electromagnetic waves with frequencies smaller than the critical frequency of ionosphere cannot be used for communication using sky wave propagation
Statement-II : The refractive index of the ionosphere becomes very high for frequency.

Options

A. Statetment-I is True, Statement-II is True , Statement-II is a correct explanation for Statement-I
B. Statement-I is True, Statement-II is True , Statement-II is NOT a correct explanation for Statement-I
C. Statement-I is True, Statement-II is False
D. Statement-I is False, Statement-II is True

Answer

To analyze the statements given in the question, we will break down the concepts of electromagnetic waves, critical frequency, and the refractive index of the ionosphere.

### Step-by-Step Solution:

1. **Understanding Statement-I**:
- Statement-I claims that electromagnetic waves with frequencies smaller than the critical frequency of the ionosphere cannot be used for communication using sky wave propagation.
- The critical frequency is the maximum frequency that can be reflected by the ionosphere. Frequencies below this critical frequency can indeed be reflected back to Earth, allowing for communication.

2. **Understanding Statement-II**:
- Statement-II states that the refractive index of the ionosphere becomes very high for certain frequencies.
- The refractive index of the ionosphere is frequency-dependent. For frequencies lower than the critical frequency, the refractive index is less than that of free space, which means these waves can be reflected.

3. **Evaluating Statement-I**:
- Since waves with frequencies lower than the critical frequency can be reflected by the ionosphere, Statement-I is incorrect. They can be used for communication as they can be reflected back to the Earth.

4. **Evaluating Statement-II**:
- Statement-II is correct. The refractive index of the ionosphere does indeed change with frequency, and for frequencies above the critical frequency, the refractive index is high, causing the waves to be refracted rather than reflected.

5. **Conclusion**:
- Statement-I is incorrect, and Statement-II is correct. Therefore, Statement-II does not provide a correct explanation for Statement-I.

### Final Answer:
- Statement-I is incorrect, and Statement-II is correct. Thus, the correct option is that only Statement-II is true.