∵Measuring the Speed of Light Galileo attempted to measure...

$\because$ Measuring the Speed of Light Galileo attempted to measure the speed of light by measuring the time elapsed between his opening a lantern and his seeing the light return from his assistant's lantern. The experiment is illustrated in FIGURE $25-38 .$ What distance, $d,$ must separate Galileo and his assistant in order for the human reaction time, $\Delta t=0.2 \mathrm{s},$ to introduce no more than a 15$\%$ error in the speed of light?

$\because$ Measuring the Speed of Light Galileo attempted to measure the
speed of light by measuring the time elapsed between his opening
a lantern and his seeing the light return from his assistant's lantern. The experiment is illustrated in FIGURE $25-38 .$ What distance,
$d,$ must separate Galileo and his assistant in order for the human
reaction time, $\Delta t=0.2 \mathrm{s},$ to introduce no more than a 15$\%$ error
in the speed of light?

Key Concepts

Speed of Light

A fundamental constant in physics, the speed of light in vacuum is the maximum speed at which information, energy, and matter can travel. It plays a central role in theories such as electromagnetism and special relativity, and its precise measurement helps validate our understanding of space and time.

Time-of-Flight Measurement

This is an experimental method for determining the speed of an object by measuring the time it takes to cover a known distance. In contexts like measuring the speed of light, the technique involves sending a light pulse over a set distance and timing its journey, which requires precise timing and distance measurements.

Measurement Uncertainty

Measurement uncertainty refers to the doubt that exists about the result of any measurement. It encompasses various sources of error, such as instrumental limitations, environmental factors, and human reaction times. Quantifying this uncertainty is critical to assess the reliability and accuracy of experimental results.

Experimental Design in Timing Experiments

Experimental design in timing-based experiments involves planning the setup to minimize errors and external influences. This includes selecting an appropriate distance between the source and detector to ensure that time delays, like reaction times or other systematic lags, do not introduce significant errors into the calculated speed, thereby enabling a more accurate determination of the constant being measured.

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