A laser is a source of very intense, monochromatic, and unidirectional beam of light. These properties of a laser light can be exploited to measure long distances. The distance of the Moon from the Earth has been. already determined very precisely using a laser as a source of light. A laser light beamed at the moon takes 2.56 s to return after rejlection at the moon's surface. How much is the radius of the lunar orbit around the earth?

To find the radius of the lunar orbit around the Earth, we can use the principles of reflection and wave motion. A laser beam is sent from the Earth to the Moon, where it reflects off the surface and travels back to the Earth.

Let the distance between the Earth and the Moon (which corresponds to the radius of the lunar orbit, $d$) be denoted as $d$.

The total time taken by the laser beam to travel to the Moon and return to the Earth is given as:
$t=2.56 \text{s}$

Because the light travels to the Moon and back, the total distance covered by the laser beam is twice the distance between the Earth and the Moon:
$\text{Total distance}=2d$

Laser light is an electromagnetic wave, and it travels at the speed of light in a vacuum or air, denoted by $c$:
$c\approx 3\times {10}^8 \text{m/s}$

Using the relationship between speed, distance, and time:
$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$
We can substitute the values into the formula:
$c=\frac{2d}{t}$

Rearranging the formula to solve for the orbit radius $d$:
$d=\frac{c\times t}{2}$

Now, substitute the given values into the equation:
$d=\frac{(3\times {10}^8 \text{m/s})\times 2.56 \text{s}}{2}$

Simplify the expression:
$d=3\times {10}^8\times 1.28 \text{m}$
$d=3.84\times {10}^8 \text{m}$

Thus, the radius of the lunar orbit around the Earth is $3.84\times {10}^8 \text{m}$.

Therefore, the correct option is 3.84 x 10⁸ m.