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, we need to calculate the maximum frequency that can return to Earth when transmitted at an angle of 60 degrees from the vertical, given that the critical frequency for the ionosphere is 30 MHz.

### Step-by-Step Solution:

1. **Understand the Relationship**:
The maximum frequency (\( f_{max} \)) that can return to Earth when transmitted at an angle (\( \theta \)) from the vertical is related to the critical frequency (\( f_c \)) by the formula:
\[ f_{max} = \frac{f_c}{\cos(\theta)} \]

2. **Identify Given Values**:
- Critical frequency (\( f_c \)) = 30 MHz
- Angle (\( \theta \)) = 60 degrees

3. **Calculate Cosine of the Angle**:
We need to find \( \cos(60^\circ) \):
\[ \cos(60^\circ) = \frac{1}{2} \]

4. **Substitute Values into the Formula**:
Now, substitute the values into the formula:
\[ f_{max} = \frac{30 \text{ MHz}}{\cos(60^\circ)} = \frac{30 \text{ MHz}}{\frac{1}{2}} \]

5. **Perform the Calculation**:
Simplifying the expression gives:
\[ f_{max} = 30 \text{ MHz} \times 2 = 60 \text{ MHz} \]

6. **Conclusion**:
The maximum frequency that can come back on Earth is:
\[ f_{max} = 60 \text{ MHz} \]

### Final Answer:
The maximum frequency that can return to Earth is **60 MHz**.