Conclusion:

Our first objective for this lab was to determine how the distance of an image formed by a “thin lens” depends on the distance between the lens and the object. For our graphs of 1/qi (cm-1) vs. 1/p0 (cm-1) (real objects) we came up with the linear eqn. 1/q(1/p) = -1.01(1/p) + 0.047 cm-1. The slope of this data would be the ratio of p to q (p/q), and is unitless. From the “thin lens” equation, we know that 1/q + 1/p = 1/f, thus 1/q = -1/p + 1/f. Therefore the y-intercept of our graph corresponds to f-1, for which f would equal 21.3cm with respect to our data. As our expected slope is -1, our %error in our data is |(-1.01 – -1) / -1| x100% = 1%. Our data was located in the first quadrant as expected.As our error bars are .002 for 1/p and .0000521 for 1/q which support the accuracy with which we collected our data.

For our second objective we set out to determine how the image height depends on the ratio of the image to object distance for images formed by a “thin lens.” For our graph of hi vs. qi/pi for the real objects, we found the best-fit linear equation of hi(cm) = -1.75(cm)(qi/po) - 0.570. The slope should correspond to the magnification of the object as we know m = -q/p. As the slope of this graph should ideally be close to -4.5, there is a great deal of error. Just in examining the data points generated, one can see the wide, and irregular distribution of our data. Our data was located in the fourth quadrant as expected. Our error bars for this data were much higher at .0228 and .32 for q/p and h respectively. Our slope did not fall within the error bars.

For the second set of data for virtual objects we came up with the eqn. 1/q(1/p) = -1.05(1/p) + 0.044 cm-1. For this data, our f equaled 22.7cm, rather close to our other set of data. Our data was located in the second quadrant as is expected. As our error bars for this were .0001 and .0003 for 1/q and 1/p respectively, we can say that our data was rather accurate.

For the second part, we came up with the eqn hi(cm) = -4.52(cm)(qi/po) - 0.045 which is very close to our expected slope of -4.5. The slope should correspond to the magnification of the object as we know m = -q/p. Our data was located in the second quadrant as expected. With error bars of .0007 and .0289 for q/p and h respectively, our data appears to be very good.

The slopes for the first portion of our data, 1/q vs. 1/p traces out the hyperbolic behavior recorded in our book of image location based on q, p and f, as a straight line.