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 it takes 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 \( t \) seconds.
- The speed of light (and hence the speed of the laser signal) is denoted as \( c \).

2. **Total Time for the Journey**:
- The total time \( t \) includes the time taken for the signal to travel to the moon and the time taken for it to return.
- Therefore, the time taken to reach the moon is \( \frac{t}{2} \) seconds.

3. **Distance Calculation**:
- The distance \( d \) to the moon can be calculated using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- Here, the speed is \( c \) and the time taken to reach the moon is \( \frac{t}{2} \).
- Thus, the distance \( d \) to the moon is:
\[ d = c \times \frac{t}{2} \]

4. **Final Expression**:
- Therefore, the distance of the moon from the observer is:
\[ d = \frac{ct}{2} \]

### Conclusion:
The distance of the moon from the observer is \( \frac{ct}{2} \).

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