Chapter 34, Problem 34.102P

DATA In setting up an experiment for a high school biology lab, you use a concave spherical mirror to produce real images of a 4.00-mm-tall firefly. The firefly is to the right of the mirror, on the mirror’s optic axis, and serves as a real object for the mirror. You want to determine how far the object must be from the mirror’s vertex (that is, object distance s) to produce an image of a specified height. First you place a square of white cardboard to the right of the object and find what its distance from the vertex needs to be so that the image is sharply focused on it. Next you measure the height of the sharply focused images for five values of s. For each s value, you then calculate the lateral magnification m. You find that if you graph your data with s on the vertical axis and 1/m on the horizontal axis, then your measured points fall close to a straight line. (a) Explain why the data plotted this way should fall close to a straight line. (b) Use the graph in Fig. P34.102 to calculate the focal length of the mirror. (c) How far from the mirror’s vertex should you place the object in order for the image to be real, 8.00 mm tall, and inverted? (d) According to Fig. P34.102, starting from the position that you calculated in part (c), should you move the object closer to the mirror or farther from it to increase the height of the inverted, real image? What distance should you move the object in order to increase the image height from 8.00 mm to 12.00 mm? (e) Explain why l/m approaches zero as s approaches 25 cm. Can you produce a sharp image on the cardboard when s = 25 cm? (f) Explain why you can’t see sharp images on the cardboard when s < 25 cm (and m is positive).

Figure P34.102