Calculating Uncertainty for Focal Length: 50mm + 3mm & 200mm + 5mm

In summary, the conversation discusses how to calculate the uncertainty associated with the focal length by using the formula 1/u + 1/v = 1/f and considering the uncertainties in u and v. Two different approaches are mentioned, one involving rearranging the formula and the other using the concept of independent errors added in quadrature. The latter approach is found to yield the correct answer.
  • #1
hexathane
1
0
Hi!

So I've stumbled upon this question asking us to calculate the uncertainty associated with the focal length.
1/u + 1/v = 1/f
u = 50mm with uncertainty 3mm
v= 200mm with uncertainty 5mm

F is calculated as 40mm, what's the uncertainty in this value?

My first approach was to rearrange the formula to make f the subject, i.e. f= uv/u+v, then i applied the formula
Δf/f = Δu/u + Δv/v +Δ(u+v)/(u+v)

Substituting values,

Δf/40 = 3/50 + 5/200 + 8/250
Δf = 4.68

However, the correct answer is 2.1. From the solutions, i understand that another approach to this question would be to calculate fmax and fmin and then add them up and divide them by two.

Puzzled as to why my earlier steps doesn't yield the correct answer though, any help would be greatly appreciated!

Thank you :-)
 
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  • #2
Independent errors are added in quadrature: http://www.physics.rutgers.edu/ugrad/389/errors.pdf
 

Related to Calculating Uncertainty for Focal Length: 50mm + 3mm & 200mm + 5mm

1. What is uncertainty calculation?

Uncertainty calculation refers to the process of quantifying the amount of uncertainty or error in a measurement or calculation. It involves identifying and evaluating all potential sources of uncertainty and combining them to calculate an overall uncertainty value.

2. Why is uncertainty calculation important?

Uncertainty calculation is important because it allows us to understand the level of confidence we can have in our measurements and calculations. It helps us to assess the reliability and accuracy of our results and make informed decisions based on them.

3. How is uncertainty calculated?

Uncertainty is calculated by identifying and quantifying each source of uncertainty and then combining them using mathematical formulas or statistical methods. The most common approach is to use the root-sum-square (RSS) method, which involves taking the square root of the sum of the squared uncertainties.

4. What are the types of uncertainty?

The two main types of uncertainty are random uncertainty and systematic uncertainty. Random uncertainty, also known as precision uncertainty, refers to the natural variation in measurements. Systematic uncertainty, also known as accuracy uncertainty, is caused by factors that consistently affect the accuracy of a measurement or calculation.

5. How can uncertainty be reduced?

Uncertainty can be reduced by improving the precision and accuracy of measurements, understanding and minimizing sources of error, and using appropriate measurement techniques and instruments. It is also important to properly document and report uncertainties to ensure transparency and reproducibility.

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