Cylindrical Lenses and Vials

Abstract

Objectives 1. Develop basic skills to identify, classify, and handle cylindrical thin and thick lenses. 2. Develop basic skills to make “at-a-glance” cylindrical lens characterization. 3. Determine the focal length of converging and diverging cylindrical lenses. 4. Determine the refractive index of the material from which a cylindrical vial is made. 5. Determine the refractive index of a liquid using a cylindrical vial. 6. Measure the spherical aberration of a cylindrical lens. 7. Formulate the limitations of the studied experimental techniques. Background Cylindrical Lenses Cylindrical lenses (Fig. 14.1) are special types of lenses used in the field of optometry to correct astigmatism, in novel visual displays, and in many other modern optical applications. A cylindrical lens lacks rotational symmetry about its optical axis and, as a consequence, has asymmetric focusing properties. As we already know, the ideal spherical lens produces a point image of a point object (for this reason a spherical lens is said to be stigmatic ). In contrast to this, a cylindrical lens produces a line image of a point object. Because of this, a cylindrical lens is astigmatic . Consider the cross-sections of a cylindrical lens in planes XZ and YZ as shown in Fig. 14.1. The cross-section in plane YZ is rectangular, while the cross-section in plane XZ is part of a circle. These cross-sections have different imaging properties. If we consider a point light source in the XZ and YZ planes, then the XZ cross-section acts as a spherical lens (Fig. 14.2a) and the YZ cross-section as a plane parallel plate (Fig. 14.2b). Now we understand why a cylindrical lens produces a line image of a point light source , as shown in Fig. 14.3. It should be noted that all the equations derived for spherical lenses can also be applied to cylindrical lenses, but only for the plane cross-section ( XZ shown in Fig. 14.1–14.3). With a certain degree of caution, the information you applied to spherical lenses and parallel plates can also be applied in experiments with cylindrical lenses.