Yesterday I posted about the lab Practicum my students did to complete their converging lens lab. Two out of three groups were able to use algebra to find the object and image distances for the setup that would produce an image three-times the size of their object.
They did not think to try and solve it graphically. Below is the graph of the students data for a lens of focal length 25 cm. the two lines leaving 0 represent the lines you get if you plot the inverse of the image distance as a function of 1/xdo, where “x” is the multiplier of the object height. For us, this was 3, hence the slopes of those lines.
Where our lens data crosses this data, is how you get object distance and image distance.
The positively rising line gives us the object and image distance for the real image that is three times the size, and the other line is still a mystery. What do you think? Positive object distance, and negative image distance. Hmmmm.