(solved)Question 2.29 of NCERT Class XI Physics Chapter 2

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 reflection at the Moon's surface. How much is the radius of the lunar orbit around the Earth ?
(Rev. 27-Mar-2023)

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Question 2.29 NCERT Class XI Physics

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 reflection at the Moon's surface. How much is the radius of the lunar orbit around the Earth ?

Physical Concept

The LASER beam is an electromagnetic beam that travels at the speed of light.

The beam travels a distance 2R, where R is radius of the earth-moon orbit.

The distance is covered at a uniform and constant speed in 2.56 seconds. Hence speed distance formula, distance = speed x time, can be applied.

Video Explanation

Please watch this youtube video for a quick explanation of the solution:

Solution

\begin{aligned} &\text{let earth moon distance} = R\\\\ &\therefore \text{distance covered} = 2R\\ &\text{time to return given as } t = 2.56 s\\ &\text{speed is of light } = c \text{ m/s}\\\\ &\text{speed is constant, so speed distance}\\ &\text{formula can be applied}\\\\ &\therefore 2R = c \times t\\\\ &\implies R = \frac 12 \times c \times t\\\\ &\implies R = \frac 12 \times 3.00 \times 10^8 \times 2.56\\\\ &\implies R = 3.84 \times 10^8 \text{ meters}\:\underline{Ans} \end{aligned}