Images from Thin Lenses
shows a thin lens with convex refracting surfaces, or sides. When rays that are parallel to the central axis of the lens are sent through the lens, they refract twice, as is shown enlarged in Fig. 35-12b. This double refraction causes therays to converge and pass through a common point F2 at a distance/from the center of the lens. Hence, this lens is a converging lens; further, a real focal point (or focus) exists at F2 (because the rays really do pass through it), and the associated focal length is f When rays parallel to the central axis are sent in the opposite direction through the lens, we find another real focal point at F] on the other side of the lens. For a thin lens, these two focal points are equidistant from the lens.
focal lengths / to be positive, just as we do with a real focus of a concave mirror. However, signs in optics can be tricky, so we had 6euer check this in Eq. 35-10. The left side of that equation is positive jf / is positive; how about the right side? We examine it term by ten. Because the index of refraction n of glass or any other material is greater than I, the term (n – I) must be positive. Because the source of the light (which is the object) is at the left and faces the convex left side of the lens, the radius of curvature rl of that side must be positive according to the sign rule for refracting surfaces. Similarly, because the object faces a concave right side of then the radius of curvature r2 of that side must be negative according to that rule.Thus, the term (llrJ – Ilr2) is positive, the whole right side ofEq. 5-10 is positive, and all the signs are consistent. Figure 35-12c shows a thin lens with concave sides. When rays that are parallel to the central axis of the lens are sent through this lens, they refract twice, as is shown enlarged in Fig. 35-12d; these rays diverge, never passing through any common point, and so this lens is a diverging lens. However, extensions of the rays do pass through a common point F2 at a distance/from the center of the lens. Hence,
the lens has a virtual focal point at F2• (If your eye intercepts some of the diverging rays, you perceive a bright spot to be at F2′ as if it is the source of the light.) Another virtual focus exists on the opposite side of the lens at FI’ symmetrically placed if the lens is thin. Because the focal points of a diverging lens are virtual, we take the
focal length/to be negative.