Chapter 24, Problem 54GP

Set Up: Use $\frac{1}{s}+\frac{1}{s\prime }=\frac{1}{f}$. A plot of $\frac{1}{f}$ versus $\frac{1}{s}$— should give a straight line with a slope of unity and a y intercept of $y_0=\frac{1}{s\prime }$.

Solve: The plot of the data is shown below.

From the best-fit line, the y intercept is 0.099 cm⁻¹. Thus, the image distance is $s\prime =\frac{1}{y_0}=\frac{1}{0.99{\text{cm}}^{\text{-1}}}$ = 1.0 cm

Reflect: From the best-fit line, the slope is 1.0179 ± 0.0126, which is close to the expected value of unity.

54. A physics student is given a set of converging lenses that have a range of focal lengths. The lab instructo asks her to position an object in front of each lens so that the image distance always has the same value, whi is specified in the lab manual. The table gives the measured object distances and the corresponding focal lengths.

f(cm)	d0 (cm)
5	10.1
6	15 3
7	22.8
8	39.2
9	90 5

Make a plot of the inverse focal length as a function of the inverse object distance Using a linear “best fit” to the data, determine the image distance that was specified in the lab manual.