Radius of curvature using spherometer

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The discussion centers on the confusion surrounding two formulas for calculating the radius of curvature using a spherometer. Participants debate the validity of both formulas, with one being derived correctly while the other raises questions about the variable "a." It is clarified that "a" in the second formula corresponds to "d" in the first formula, which leads to further confusion about their equivalence. Despite the differences in presentation, the formulas are intended to yield the same result for radius (r=R). The conversation highlights the need for clarity in understanding the variables used in each formula.
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which formula is correct?
spherometer.jpg
or
b55a8e505eea5106a0ee5bdbc5daa016.png
 
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leojun said:
which formula is correct?
The one of the picture looks correctly derived. Where does the other one come from, and what is "a"?
 
A.T. said:
The one of the picture looks correctly derived. Where does the other one come from, and what is "a"?

We use second formula instead of the first formula to find the radius of curvature using spherometer.
"a" in the second formula is the same as "b" in the first formula.
The first formula is correct but i don't get why we use second formula instead of first.
The two formula's are supposed to be the same r=R,but why are they different?
 
leojun said:
"a" in the second formula is the same as "b" in the first formula.
I see no "b" in the first formula.
 
A.T. said:
I see no "b" in the first formula.
SORRY,"a" in the second formula is the same as "d" in the first formula
 
A.T. said:
what is "a"?
"a" is the side length of the triangle, or distance between two of the three points.
 
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leojun said:
SORRY,"a" in the second formula is the same as "d" in the first formula
I don't think so. I think Bystander is right and the formulas are equivalent.
 
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