# Which of these 2 methods for calculating the focal length of a concave mirror is more accurate?

I have done an experiment to measure $$f$$ the focal length of a concave mirror.

I have a list of 8 values for $$u$$ the object distance and 8 values for $$v$$ the corresponding image distance.

I calculated the focal length using 2 methods.

Method 1:

I got 8 values for $$f$$ using the formula $$f=\frac{uv}{u+v}$$

All values fell within $$2\sigma$$ so I used them all to find an average value.

Method 2:

I graphed $$\frac{1}{u}$$ against $$\frac{1}{v}$$ and from the average of the $$x$$ and $$y$$ intercepts of the regression line I found the focal length.

My question is:

Which of these 2 methods is more accurate?

Is there some way of qualitatively calculating the accuracy of each method?

NB: I did use the third method of approximating the focal length by focusing a distance object on some paper but let's ignore that method for the purpose of comparing the 2 methods in question.

• All values fell within a standard deviation of 2σ This doesn't really make sense. A standard deviation is σ.
– user4552
Commented Mar 9, 2019 at 19:31
• @BenCrowell You are right. Edited accordingly. Commented Mar 9, 2019 at 19:39