How Did Galileo's Lantern Experiment Attempt to Measure the Speed of Light?

[Flyfishinva]

I'm having trouble with a proble I'm trying to complete. The Problem states:

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 25-24. What distance, d, must separate Galileo and his assistant in order for the human reaction time, t = 0.2 s, to introduce no more than a 18% error in the speed of light?

The only way I can think to do the problem is with, time = distance/speed of light. Time would equal 0.1 s and speed of light minus 18% error (I think its minus, because the error would make the velocity seem slower) would be 2.46E8 m/s. d= 0.1s(2.46E8 m/s) = 2.46E7 m (the wrong answer). Any suggestions? Thanks

 

[Andrew Mason]

I'm having trouble with a proble I'm trying to complete. The Problem states:

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 25-24. What distance, d, must separate Galileo and his assistant in order for the human reaction time, t = 0.2 s, to introduce no more than a 18% error in the speed of light?

The only way I can think to do the problem is with, time = distance/speed of light. Time would equal 0.1 s and speed of light minus 18% error (I think its minus, because the error would make the velocity seem slower) would be 2.46E8 m/s. d= 0.1s(2.46E8 m/s) = 2.46E7 m (the wrong answer). Any suggestions? Thanks

The measured speed would be [itex]c_{m} = d/t[/itex] where t = total elapsed time which includes the reaction time of .2 sec.

The actual speed of the light would be [itex]c = d/(t-t_r)[/itex]

So the question asks: what value of d will make the difference [itex]c-c_m[/itex] less than or equal to .18c? That means that [itex]c_m \ge .82c [/itex].

Use the relationship: [itex]t - t_r = d/c[/itex] and [itex]t = d/c + t_r[/itex]

AM

 

[kyle8921]

I would like to address your question regarding Galileo's attempt to measure the speed of light using his lantern experiment. First of all, it is important to note that Galileo's experiment was conducted in the 17th century and our understanding of the speed of light has significantly advanced since then.

To accurately measure the speed of light, we now use sophisticated equipment and techniques such as the use of lasers and mirrors. Galileo's experiment, while innovative at the time, is not considered a reliable method for measuring the speed of light.

However, in response to your specific question, I would suggest approaching the problem using the equation velocity = distance/time, where the velocity is the speed of light with an 18% error, the time is the human reaction time of 0.2 seconds, and the distance is what we need to calculate. Rearranging the equation, we get distance = velocity x time. Plugging in the values, we get distance = (2.46E8 m/s)(0.2 s) = 4.92E7 m.

It is important to note that this calculation assumes that the human reaction time is the only source of error in the experiment. In reality, there are other factors that can introduce error, such as the accuracy of the lanterns and the distance between them. Therefore, this calculation should be taken with caution and is not an accurate representation of the speed of light.

In conclusion, while Galileo's experiment was a significant step in our understanding of the speed of light, it is not a reliable method for measurement. As scientists, we continue to use advanced techniques to accurately measure the speed of light and expand our knowledge of this fundamental constant.