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Inquiry: Diverging Lens

Purpose: To measure the focal length of a diverging lens.


The relation between the object distance so, the image distance si, and the focal length f of a lens is given by the fundamental lens formula:

1/f = 1/ so + 1/ si

One standard practice in optics is to use the optical center of the lens as the origin and to measure distances to the left as negative and distances to the right as positive, and to let the incident rays travel from left to right. Consequently, so is positive for real objects and negative for virtual objects; si is positive for real images and negative for virtual images; and f is positive for converging lenses and negative for diverging lenses. In order to find the focal length of a diverging lens we shall use a converging lens ahead of it to converge the rays before they reach the diverging lens. If a converging lens forms a real image at I (see picture below), the introduction of the diverging lens between this lens and the real image will cause the image to be formed farther away at I'. By taking the distance from the diverging lens to the position of I as the object so and to the position of I' at the image distance si, the lens formula may be used to determine the focal length f of the diverging lens.

Mount the converging lens on the optical bench between the object box and the cardboard screen and adjust the lens and screen until a sharp image is formed. Determine at this point whether a reduced or enlarged image is preferable. This image is located at I. Observe the edges of the image closely while slowly moving the screen through the position of sharpest focus. Insert a diverging lens between the converging lens and the screen and again move the screen until a sharp image is formed. This is the position I'. Record the values of so and si in your notebook and calculate the focal length. Be sure to use + and - signs correctly. Make another measurement of f by varying so and si. Record all data and find the average focal length of the lens.