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FOR. mate, from the lens proof we discussed last week, could

FOR RYAN. Hi mate, from...
FOR RYAN. Hi mate, from the lens proof we discussed last week, could you provide me a new copy with the "t" values changed to a "w" (for width) and the "w" values changed to a "l" (length). That is more appropriate for my application of the formula. And then would you provide a worked example (using your formula) for a width of 2 and a length of 6...answer in cm2. and another worked example for a width of 4 and a length of 8.
Thanks
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Answered in 36 minutes by:
11/9/2017
Ryan
Ryan, Engineer
Category: Math Homework
Satisfied Customers: 9,110
Experience: B.S. in Civil Engineering
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Hi,

Ok, no problem. I'll get those to you as soon as I can.

Regards,

Ryan

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Hi again,

Here is a link to the reworked derivation, with the requested example calculations.

Lens3

As before, please let me know if you have any additional questions about this.

Thanks,

Ryan

Ryan
Ryan, Engineer
Category: Math Homework
Satisfied Customers: 9,110
Experience: B.S. in Civil Engineering
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Customer reply replied 1 month ago
That's fantastic, thanks Ryan.
Still no luck with some sort of a source for the formula? Surely some sort of maths book somewhere has dealt with the area of a "lens"?

I'm sorry about the delayed reply. You last message arrive on my end at 2:15 in the morning. I've been running around all day and am just now getting back online to get caught up.

No, I haven't been able to find an online source of this type of formula. Part of the difficulty is filtering out the search results to avoid things like camera lenses, articles about lenses that deal with the physics of how light is bent, etc.

The other part of the problem is that the few references that are available tend to model the lens as the intersection two overlapping circles, and calculate the area of overlap from the radii of the two circles and the distance between the centers of the circles. This solution has the added benefit of not requiring that both sides of the lens have the same curvature, as the solution that I developed does. But the solution isn't useful to you since you don't know what the radius is, or what the distance between the centers of curvature are.

I haven't been able to find any published source online that deals with the desired area in terms of the length and width of the lens itself, instead of the above-mentioned circular radii.

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