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 of the ionosphere is 30 MHz.

### Step-by-Step Solution:

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

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

3. **Calculate \( \cos(60^\circ) \):**
- We know that:
\[ \cos(60^\circ) = \frac{1}{2} \]

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

5. **Simplify the Expression:**
- Dividing by \( \frac{1}{2} \) is equivalent to multiplying by 2:
\[ f_{max} = 30 \text{ MHz} \times 2 = 60 \text{ MHz} \]

6. **Final Result:**
- Therefore, the maximum frequency that can come back to Earth is:
\[ f_{max} = 60 \text{ MHz} \]

### Conclusion:
The maximum frequency that can return to Earth when transmitted at an angle of 60 degrees from the vertical is **60 MHz**.