Problem 54 - University Physics with Modern Physics

Question

A laser beam takes 50.0 ms to be reflected back from a totally reflecting sail on a spacecraft. How far away is the sail?

Step-by-Step Solution

Answer

Answer: The distance between the laser source and the reflecting sail is \(7.50 \times 10^6\) meters.

Step 1: Convert time to seconds

The time is given in milliseconds (ms), so we first need to convert it to seconds (s) using this conversion factor: 1 s = 1000 ms So, 50.0 ms = 50.0/1000 s = 0.050 s.

Step 2: Write down the speed of light

The speed of light \(c\) in a vacuum is approximately: \(c = 3.00 \times 10^8\) m/s.

Step 3: Calculate the total distance the light travels

The laser beam travels to the sail and back; thus, it covers twice the distance between the source and the sail. We can find the total distance traveled by the light using the formula: distance = speed x time total distance = \(c \times t\), where \(t\) is the time taken by the light. total distance = \((3.00 \times 10^8 \text{ m/s}) \times (0.050 \text{ s})\) total distance = \(1.50 \times 10^7\) m

Step 4: Find the distance between the laser source and the sail

Since the laser beam travels to the sail and back, the distance to the sail is half of the total distance the light travels. Therefore: distance to the sail = total distance / 2 distance to the sail = \((1.50 \times 10^7 \text{ m}) / 2\) distance to the sail = \(7.50 \times 10^6\) m So, the distance between the laser source and the reflecting sail is \(7.50 \times 10^6\) meters.

Key Concepts

Speed of Light

The speed of light, often represented by the symbol \(c\), is a fundamental constant in physics. It defines how fast light travels through a vacuum. The speed of light is approximately \(3.00 \times 10^8\) meters per second (m/s). This value is crucial in various fields of science, not just physics but also astronomy and information technology.
Light's speed is essential when studying the universe because it helps calculate distances to celestial objects and understand cosmic events. It is also a key factor in technologies involving laser, optics, and telecommunications. In this exercise, the speed of light is used to determine the distance traveled by a laser beam.

Time Conversion

In physics, accurate measurements are crucial. This includes the ability to convert time from one unit to another. Timely conversion helps maintain consistency and avoid errors in calculations involving speed and distance.
For example, in the given exercise, the time of 50.0 milliseconds (ms) needs to be converted to seconds (s) because the speed of light is given in meters per second.

• To convert from milliseconds to seconds, divide the time value by 1000 (since 1 second equals 1000 milliseconds).
• Here, 50.0 ms is converted to 0.050 s.

This conversion is straightforward yet essential for ensuring the calculations align with the units of speed to find the correct distance.

Reflection Measurement

Reflection measurement involves understanding how light or other waves bounce off a surface. In scenarios like laser ranging, it's important to measure the time taken for light to hit an object and reflect back. This information helps calculate the distance to the object.
For instance, when a laser beam is emitted towards a reflecting sail on a spacecraft, it travels to the sail and reflects back. By knowing the time taken for this round trip and using the speed of light, the total distance covered by the laser can be calculated.

• This includes both the journey to the object and the return trip.
• The actual one-way distance is half of this calculated round-trip distance.

Such measurements are vital in fields like astronomy, meteorology, and surveying.

Laser Beam Physics

Laser beam physics focuses on the behavior of laser light, which is uniquely coherent and monochromatic. This means that laser beams travel in straight lines with very little spread, making them ideal for accurate distance measurements in physics experiments.
Lasers are widely used in ranging because they produce narrow, concentrated beams that can travel long distances with minimal dispersion.

• In laser ranging, a laser beam is directed towards a reflective target.
• The time taken for the beam to return after hitting the target is measured.

Using the known speed of light, this time measurement can then be used to calculate the distance to the target. This technique is used in various applications from mapping the Earth's surface with LIDAR to measuring distances to the Moon.