Radius of curvature using spherometer

[leojun]

Main Question or Discussion Point

which formula is correct?

or

 

[A.T.]

which formula is correct?

The one of the picture looks correctly derived. Where does the other one come from, and what is "a"?

 

[leojun]

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?

 

[A.T.]

"a" in the second formula is the same as "b" in the first formula.

I see no "b" in the first formula.

 

[leojun]

I see no "b" in the first formula.

SORRY,"a" in the second formula is the same as "d" in the first formula

 

[Bystander]

what is "a"?

"a" is the side length of the triangle, or distance between two of the three points.

 

[A.T.]

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.