A laser signal sent towards the moon returns after t seconds. If c is the speed of light then the distance of the moon from the observer is

Options

A. ct
B. `ct^(2)`
C. `ct^(1)`
D. ct/2

Explanation

To find the distance of the moon from the observer based on the time taken for a laser signal to travel to the moon and back, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
- A laser signal is sent towards the moon and returns after a time \( t \) seconds.
- The speed of light is denoted as \( c \).

2. **Distance Calculation**:
- Let \( x \) be the distance from the observer to the moon.
- When the laser signal is sent, it travels to the moon and then returns back to the observer. Therefore, the total distance traveled by the laser signal is \( 2x \).

3. **Using the Formula for Distance**:
- The relationship between distance, speed, and time can be expressed as:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- In this case, the distance traveled by the laser light is \( 2x \), the speed is \( c \), and the total time taken for the round trip is \( t \). Thus, we can write:
\[ 2x = c \times t \]

4. **Solving for \( x \)**:
- To find the distance \( x \), we rearrange the equation:
\[ x = \frac{c \times t}{2} \]

5. **Final Result**:
- Therefore, the distance of the moon from the observer is:
\[ x = \frac{ct}{2} \]

### Conclusion:
The correct answer is \( \frac{ct}{2} \).