Light travels at a speed of about 3.0 108 m/s.
(a) How many miles does a pulse of light travel in a time interval of 0.1 s, which is about the blink of an eye?
(b) Compare this distance to the diameter of Earth.
The correct answer and explanation is :
We start with the given speed of light:
[
c = 3.0 \times 10^8 \text{ m/s}
]
(a) Distance Light Travels in 0.1 Seconds
The distance traveled by light in a given time interval ( t ) is found using:
[
\text{distance} = \text{speed} \times \text{time}
]
Substituting ( t = 0.1 ) s:
[
d = (3.0 \times 10^8 \text{ m/s}) \times (0.1 \text{ s})
]
[
d = 3.0 \times 10^7 \text{ m}
]
To convert this to miles, we use:
[
1 \text{ mile} = 1609 \text{ m}
]
[
d = \frac{3.0 \times 10^7 \text{ m}}{1609 \text{ m/mile}}
]
[
d \approx 1.86 \times 10^4 \text{ miles}
]
Thus, light travels approximately 18,640 miles in 0.1 seconds.
(b) Comparison to Earth’s Diameter
The average diameter of Earth is about 12,742 km or 7,918 miles.
Now, let’s compare:
[
\frac{\text{distance traveled by light in 0.1 s}}{\text{Earth’s diameter}} = \frac{18,640}{7,918} \approx 2.35
]
This means that in just 0.1 seconds, light could travel more than twice the diameter of Earth.
Explanation (300 Words)
Light travels at an incredible speed of approximately 300 million meters per second. To put this into perspective, we calculated how far light travels in just 0.1 seconds, which is roughly the time it takes to blink. The result is 30 million meters, or about 18,640 miles.
To understand this distance better, we compared it to the diameter of Earth, which is 7,918 miles. The result shows that in just a tenth of a second, light could travel more than twice across the entire planet. This means that if a pulse of light started from one side of the Earth, it would reach the other side and then travel back again before the blink of an eye is completed.
This calculation highlights the immense speed of light, which is fundamental to modern physics and technology. For example, fiber-optic communication relies on light traveling through glass cables to transmit data almost instantaneously over long distances. Similarly, astronomical distances are measured using the speed of light, such as the time it takes for light from the Sun to reach Earth, which is about 8 minutes and 20 seconds.
In summary, the speed of light is so fast that in just 0.1 seconds, it can travel a distance greater than twice the width of our planet. This comparison helps us grasp just how vast and fast light really is in everyday terms.