Could Paul Revere discern if there were one or two lanterns?

[Plasmosis1]

"one if by land and two if by sea" is the famous saying of Paul Revere when he was a certain distance away from a signal sent from the people of old North Church in Boston on the night of April 18, 1775. if the average human pupil has a diameter of 4mm at night and the lanterns had a predominant wavelength of 580 nm how far away (in miles) was Paul Revere when he received the signal about the approaching British on that fateful night? assume he was at a minimum distance of .5 m and neglect any other influences- including the shortening of the wavelength in his eye (which does not change the answer). could he actually discern if there were one or two lanterns? Show work for why or why not.

Useful equation: theta_min= 1.22*wavelength/diameter

I don't believe that there is enough information for this problem. You have two variables, distance from the lanterns and the angle created between the lanterns. Any help would be appreciated.

 

[barryj]

I think the equation gives the resolving power of the eye in radians. This comes out to be 1.76E-4 radians. I would think the lanterns would be 0.5 meters apart. Now you can determine how far away you can be to resolve the two lanterns., yes??

 

[rude man]

I think the equation gives the resolving power of the eye in radians. This comes out to be 1.76E-4 radians. I would think the lanterns would be 0.5 meters apart. Now you can determine how far away you can be to resolve the two lanterns., yes??

The problem's wording is terrible but I think you have the right approach to it nonetheless.

 

[barryj]

I think you have a similar question on this forum about can a spy satellite see a license plate.

 

[Nickie]

I would first clarify the question and gather more information to accurately answer it. There are a few key factors that need to be considered in order to determine if Paul Revere could discern one or two lanterns from a distance.

First, we need to know the distance between Paul Revere and the signal sent from the old North Church. Without this information, we cannot accurately calculate the angle between the two lanterns and determine if they would appear as one or two separate lights to Paul Revere.

Additionally, the angle of vision also plays a role in determining if Paul Revere could discern one or two lanterns. The average human pupil diameter of 4mm at night is only applicable if the lanterns are directly in front of Paul Revere. As the angle of vision increases, the apparent size of the pupil decreases, making it more difficult to discern separate lights.

Furthermore, the wavelength of light and its impact on human vision is also a complex factor. While the predominant wavelength of 580nm can help determine the color of the light, it does not necessarily indicate how it will appear to Paul Revere from a distance. The human eye has a range of sensitivity to different wavelengths, and the visual acuity of an individual can also vary.

Therefore, without the specific distance and angle between Paul Revere and the signal, it is impossible to accurately determine if he could discern one or two lanterns. The equation provided may be useful in calculating the angle between the two lanterns, but it cannot be applied without the necessary information.

In conclusion, while we know that Paul Revere used the phrase "one if by land and two if by sea" to communicate the number of lanterns, it is not possible to definitively say if he could discern one or two lanterns from a distance without more information.