A laser beam is sent to the moon and reflected back to earth by a mirror placed on the moon by an astronaut. If the moon is at 3,84,000 km distance from earth, how long does it take the light to make the round trip?

Options

A. 5 min
B. 2.5 min
C. 2.5 s
D. 500 s

Answer

To solve the problem of how long it takes for a laser beam to travel to the moon and back, we can follow these steps:

### Step 1: Understand the Given Information
- Distance from Earth to the Moon (one way): \( d = 3.84 \times 10^5 \) km
- Convert this distance into meters:
\[ d = 3.84 \times 10^5 \text{ km} = 3.84 \times 10^8 \text{ m} \]
- Speed of light:
\[ c = 3 \times 10^8 \text{ m/s} \]

### Step 2: Calculate the Round Trip Distance
Since the laser beam travels to the moon and back, the total distance for the round trip is:
\[ \text{Total distance} = 2 \times d = 2 \times 3.84 \times 10^8 \text{ m} = 7.68 \times 10^8 \text{ m} \]

### Step 3: Use the Speed of Light to Find Time
We can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the total distance and the speed of light into the formula gives:
\[ T = \frac{7.68 \times 10^8 \text{ m}}{3 \times 10^8 \text{ m/s}} \]

### Step 4: Perform the Calculation
Calculating the time:
\[ T = \frac{7.68}{3} \text{ seconds} = 2.56 \text{ seconds} \]

### Conclusion
The time taken by the light for the round trip to the moon and back is:
\[ T = 2.56 \text{ seconds} \]