# Propagation of Error for Sodium Doublet Lines

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In summary, the conversation revolved around the use of the equation Δλ = (λ^2 / 2Δd) in a lab where the goal was to calculate the separation of sodium D doublet lines. The only uncertain value in the equation was Δd, leading to confusion about how to propagate the error. The person asked for advice and was reminded that they should have been given instructions or formulae for error propagation.
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Homework Statement
I need help propagating the error in a formula
Relevant Equations
Δλ = (λ^2
/ 2Δd)
The equation we used in this lab was Δλ = (λ^2 / 2Δd) where Δλ is the separation of the sodium D doublet lines and is the value we're trying to calculate, λ^2 is the wavelength of sodium light given in the lab manual (589 nm) and Δd is the distance one of the mirror moves to go from one faint spot in the interference pattern to the next.

The part I'm confused with is we've been told to propagate the error for Δλ but the only value we have in the formula that has an uncertainty is Δd. I've tried many different formulae to propagate the error but I keep getting wrong units, no units, etc..

If someone could give me some advice that would be awesome. Thank you!

Surely you wouldn’t be asked to propagate error without someone at sometime telling you how to propagate error. Do you not have some formulae or instructions related to error propagation?

## 1. What is the Propagation of Error for Sodium Doublet Lines?

The Propagation of Error for Sodium Doublet Lines refers to the calculation of uncertainty or error in the measurement of the wavelength of the sodium doublet lines. These lines are two closely spaced spectral lines in the yellow region of the electromagnetic spectrum, and their measurement is important in various fields of science, including astronomy and atomic physics.

## 2. Why is the Propagation of Error important for Sodium Doublet Lines?

The Propagation of Error is important because it allows us to quantify the uncertainty in the measurement of the wavelength of the sodium doublet lines. This uncertainty can arise from various sources, such as instrumental errors, environmental factors, and human error. By understanding and accounting for these sources of error, we can improve the accuracy and reliability of our measurements.

## 3. How is the Propagation of Error calculated for Sodium Doublet Lines?

The Propagation of Error is calculated using a mathematical formula that takes into account the uncertainties in the various factors that contribute to the overall error in the measurement. This formula involves taking the square root of the sum of the squares of the individual uncertainties. It is important to note that this calculation assumes that the errors are independent and normally distributed.

## 4. What are the factors that contribute to the error in measuring the wavelength of Sodium Doublet Lines?

There are several factors that can contribute to the error in measuring the wavelength of the sodium doublet lines. These include instrumental errors, such as calibration and resolution limitations of the spectrometer, environmental factors like temperature and pressure variations, and human errors, such as misalignment of the spectrometer or misreading of the measurement.

## 5. How can we reduce the error in measuring the wavelength of Sodium Doublet Lines?

To reduce the error in measuring the wavelength of the sodium doublet lines, we can take several steps. These include using high-quality instruments with better resolution and calibration, controlling environmental factors to minimize their impact, and using multiple measurements and statistical analysis to account for human error. Additionally, proper training and techniques can also help in reducing the error in measurements.

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