Optics. Optical systems Geometrical optics. Optical systems 1. Thin lens equation Consider a lens having an index of refractionn and two spherical surfaces with radii of curvature R1 and R2, as in Figure. An object is placed at point O at a distance p in front of surface. The focal length f of a thin lens is the image distance that corresponds to an infinite object distance `R1 R2 C2 C1 %3D f– lens focal length (m); p – distance from the object to the lens or object distance (m); q – distance from the image to the lens or image distance (m). Sign Conventions for Thin Lenses p is positive if object is in front of lens (real object). p is negative if object is in back of lens (virtual object). q is positive if image is in back of lens (real image). q is negative if image is in front of lens (virtual image). ICI fis positive if the lens is converging. fis negative if the lens is diverging. (a) (b) 2. Magnification of Images The lateral magnification of the lens is defined as the ratio of the image height H to the object height h: Н M = H – image height (m); h – object height (m), p – distance from the object to the lens or object distance (m); g- distance from the image to the lens or image distance (m). 3. Optical power of the lens: 1 P = Here fis the focal length. Optical power P is measured in Dioptres (dptr). 4. Lens makers’ equation: = (n – 1) R1 Rj and R2 – radii of curvature of front and back surface of the lens (m), n – lens index of refraction. 5. Magnification of the system of n lens combination м - М,-М, ...м, M - total magnification, Mn – magnification of individual lens. 6. Ray diagrams for thin lenses Converging lens Optics. Optical systems Back Front Front Back (a) (b) Diverging lens Front Back (c) Ray diagrams for locating the image formed by a 3 thin lens. (a) When the object is in front of and outside the object focal point F1 of a converging lens, the image is real, inverted, and on the back side of the lens. (b) When the object is between F1 and a converging lens, the image is virtual, upright, larger than the object, and on the front side of the lens. (c) When an object is anywhere in front of a diverging lens, the image is virtual, upright, smaller than the object, and on the front side of the lens. 7. The compound microscope The microscope has extended human vision to the point where we can view previously unknown details of incredibly small objects. The overall magnification of the compound microscope M is defined as the 25 ст product of the objective M, = - and eyepiece M. = fo magnifications: fe L /25 ст M = M,M. = here fo – focal length of the objective, fe – focal length of the eyepiece, L - distance between the objective and the eyepiece. Objective Eyepiece So F. (a) (b)