The table below shows measurements of magnification versus...

The table below shows measurements of magnification versus object distance for a lens. Determine a quantity that, when you plot object distance against it, should give a straight line. Make your plot, establish a best-fit line, and use your line to find the focal length of the lens. $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Object distance, } s(\mathrm{~cm}) & 10.1 & 29.2 & 51.6 & 78.3 & 98.9 \\ \hline \text { Magnification, } M & 1.31 & 4.77 & -4.38 & -1.27 & -0.724 \\ \hline \end{array} $$

The table below shows measurements of magnification versus object distance for a lens. Determine a quantity that, when you plot object distance against it, should give a straight line. Make your plot, establish a best-fit line, and use your line to find the focal length of the lens.
$$
\begin{array}{|l|c|c|c|c|c|}
\hline \text { Object distance, } s(\mathrm{~cm}) & 10.1 & 29.2 & 51.6 & 78.3 & 98.9 \\
\hline \text { Magnification, } M & 1.31 & 4.77 & -4.38 & -1.27 & -0.724 \\
\hline
\end{array}
$$

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Key Concepts

Graphical Analysis and Best-Fit Line

Graphical analysis involves plotting experimental data to reveal underlying relationships between variables. By fitting a best-fit line to a linearized dataset, key parameters—such as the focal length in applications of the thin lens equation—can be determined from the slope and intercept of the line.

Magnification

Magnification is defined as the ratio of the image size to the object size and is also given by the negative ratio of image distance to object distance (M = -s'/s). This concept connects the spatial properties of an image to the distances involved in its formation.

Thin Lens Equation

The thin lens equation relates the object distance, image distance, and the focal length of a lens through the relation 1/s + 1/s' = 1/f. This fundamental equation underpins much of geometric optics and is used to understand and predict how lenses form images.

Data Linearization

Data linearization is a technique used to transform a non?linear relationship into a linear one by plotting appropriate transformed variables. This makes it easier to analyze the data, extract parameters, and perform a linear regression.

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