# Physics and Astronomy Labs/Optics: Thin lens equation (ray diagram)

1. Each student makes a drawing similar to figure below and measures S1, S2, and f. Enter those values on a spreadsheet, making columns for each entry.
2. To the right of this column, create three more columns that contain: S1/f, S2/f, and f/f (each entry in the last column is of course unity. These three columns represent the image and object distances, as measured in focal lengths.
3. Let x = S1/f and let y = S2/f, and make a plot of x versus y.
4. Now make a plot of X=1/x and Y=1/y. When doing such calculations by hand, use "bars" to distinguish upper and lower case letters, as shown to the right.
5. S1 represents the "object distance". Carefully define this distance by fully describing the two endpoints. The formula is only valid for an infinitely thin lens, research which part of the lens is used to define this endpoint. Research the Wikipedia articles and see if you can find a place where this distance is defined. The best way to search Wikipedia is NOT the Wikipedia search bar. Use Google or its equivalent instead. A list of search words includes thin lens and paraxial approximation

${\frac {1}{S_{1}}}+{\frac {1}{S_{2}}}={\frac {1}{f}}$ relates the focal length f of the lens, the image distance S1, and the object distance S2. The figure depicts the situation for which (S1, S2, f) are all positive: (1)The lens is converging (convex); (2) The real image is to the right of the lens; and (3) the object is to the left of the lens. If the lens is diverging (concave), then f < 0. If the image is to the left of the lens (virtual image), then S2 < 0 .