If critical frquency for ionosphere is 30MHz.Calculate the maximum frequency which can comeback on earth if transmitted at an angle `60^(@)` from vertical.

Options

A. 30 MHz
B. 60MHz
C. 40MHz
D. 15MHz

Answer

To solve the problem of finding the maximum frequency that can return to Earth when transmitted at an angle of 60° from the vertical, we will use the relationship between critical frequency and the angle of transmission.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- The critical frequency (fc) for the ionosphere is given as 30 MHz.
- The angle of transmission (θ) is 60° from the vertical.

2. **Use the Formula for Maximum Usable Frequency (FM):**
The formula to calculate the maximum usable frequency (FM) when transmitted at an angle θ is:
\[ FM = \frac{fc}{\sec(\theta)} \]
where:
- \( fc \) is the critical frequency,
- \( \sec(\theta) \) is the secant of the angle θ.

3. **Calculate Secant of the Angle:**
- For θ = 60°, we know that:
\[ \sec(60°) = \frac{1}{\cos(60°)} = \frac{1}{0.5} = 2 \]

4. **Substitute Values into the Formula:**
- Now, substitute the values into the formula:
\[ FM = \frac{30 \text{ MHz}}{\sec(60°)} = \frac{30 \text{ MHz}}{2} = 60 \text{ MHz} \]

5. **Conclusion:**
- The maximum frequency that can come back to Earth when transmitted at an angle of 60° is **60 MHz**.

### Final Answer:
The maximum frequency that can come back on Earth is **60 MHz**.