(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculating focal lengths of lenses.

s = 144.7 ± 5.52 mm

s' = 86.0 + 0.71 mm

2. Relevant equations

Focal Length

f = (s)(s') / ( s + s' )

Adding/Subtracting two numbers with uncertainties

A + B ± root [ (±A)^2 + (±B)^2 ]

Multiplying/Dividing

AB ± root [ (±A/A)^2 + (±B/B)^2) ]

3. The attempt at a solution

I have:

s = 144.7 ± 5.52 mm

s' = 86.0 + 0.71 mm

and am getting:

f = 53.94 ± 0.02412 mm

My question is, does it make sense that the uncertainty that was obviously significant at the start (5.52mm uncertainty in a 144.7mm magnitude) became so miniscule at the end? The way I am calculating this is

1) Calculating numerator and denominator of focal length equation separately

-Top = ( s * s' ) and get uncertainty of 0.039mm using the uncertainty multiplication rule

-Bot = ( s + s' ) and get uncertainty of 5.57mm using the uncertainty addition rule.

2) Then I divide the top by the bottom apply the uncertainty division rule.

Am I doing everything correctly?

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# Homework Help: Large Uncertainty Became Unsignificant After Calculations?

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