Radius of curvature using spherometer

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SUMMARY

The discussion centers on the correct formulas for calculating the radius of curvature using a spherometer. Participants confirm that the second formula is preferred for this calculation, despite both formulas being theoretically equivalent. The variable "a" in the second formula corresponds to "d" in the first formula, which represents the side length of the triangle formed by the spherometer's points of contact. Clarification on these variables is essential for accurate application of the formulas.

PREREQUISITES
  • Understanding of geometric principles related to triangles
  • Familiarity with spherometers and their applications
  • Knowledge of mathematical formulas for curvature
  • Basic algebra for manipulating equations
NEXT STEPS
  • Research the derivation of the radius of curvature formulas in optics
  • Explore the practical applications of spherometers in material science
  • Learn about the geometric properties of triangles in relation to curvature
  • Study the differences between various curvature measurement techniques
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Students and professionals in physics, engineering, and material science who are involved in curvature measurements and geometric analysis will benefit from this discussion.

leojun
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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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