Radius of curvature using spherometer

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Discussion Overview

The discussion revolves around the formulas used to calculate the radius of curvature using a spherometer. Participants are examining the derivation and equivalence of two different formulas, as well as clarifying the variables involved.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question which formula is correct for calculating the radius of curvature using a spherometer.
  • One participant notes that the formula depicted in a picture appears correctly derived, but seeks clarification on the origin of the other formula and the meaning of variable "a."
  • Another participant states that "a" in the second formula corresponds to "b" in the first formula, while expressing confusion over why the second formula is preferred despite the first being deemed correct.
  • There is a claim that both formulas should yield the same result (r=R), yet participants note discrepancies between them.
  • One participant asserts that "a" in the second formula is actually the same as "d" in the first formula, prompting further clarification on the definitions of these variables.
  • Another participant defines "a" as the side length of a triangle or the distance between two of the three points involved in the measurement.
  • There is a disagreement regarding the equivalence of the formulas, with one participant supporting the idea that they are equivalent, while another expresses skepticism about this claim.

Areas of Agreement / Disagreement

Participants do not reach a consensus on which formula is correct or whether the two formulas are equivalent. Multiple competing views remain regarding the definitions of variables and the appropriateness of each formula.

Contextual Notes

Participants express uncertainty about the definitions of variables "a," "b," and "d," and how they relate to the formulas. There is also a lack of clarity regarding the derivation of the formulas and their equivalence.

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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