Optics. Optical systems Geometrical optics. Optical systems 1. Thin lens equation Consider a lens having an index of refraction n and two spherical surfaces with radii of curvature Ri and R2, as in Figure. An object is placed at point O at a distance p in front of surface. The focal length fof a thin lens is the image distance that corresponds to an infinite object distance 1 1, 1 f- lens focal length (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). Sign Conventions for Thin Lenses pis positive if object is in front of lens (real object). pis megative if object is in back of lens (virtual object). q is positive if image is in back of lens (real image). q is megative if image is in front of lens (virtual image). fis pasitive if the lens is converging. fis megative if the lens is diverging. al 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); q – distance from the image to the lens or image distance (m). 3. Optical power of the lens: Here fis the focal length. Optical power P is measured in Dioptres (dptr). 4. Lens makers' equation: 1) Ri and R: – 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, M, – magnification of individual lens. 6. Ray diagrams for thin lenses Converging lens Optics. Optical systems Back Front Front Back (a) (b) Diverging lens Front Rack 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 F, 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 mieroscope 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 product of the objective M, =- and eyepiece Mẹ = 25 cm fe magnifications: M = M,M. =- here fo - focal length of the objective, fe - focal length of the eyepiece, L - distance between the objective and the eyepiece. Objecthe Eyepiece (a) (b)