LECTURE 16 THIN LENSES – RAY TRACING Instructor: Kazumi Tolich Lecture 16 2 ¨ 18.4 Image formation by refraction ¨ 18.5 Thin lenses: ray tracing ¤ Converging lenses ¤ Real images ¤ Magnification ¤ Virtual images ¤ Diverging lenses Quiz: 18.4-1 18.4 Image formation by refraction ¨ The optical axis is the line through the object and perpendicular to the boundary. ¨ Using Snell’s law and geometry, you can show that the image distance is given by � �" = % � �& 18.5 Thin lenses: ray tracing ¨ A lens uses refraction of light rays at curved surfaces to form an image. ¨ Ray tracing is a pictorial method used to understand image formation. Quiz: 18.5-1 18.5 Thin lenses: ray tracing – focal point and focal length ¨ The incoming rays parallel to the optical axis converge at (converging lens) or appear to diverge from (diverging lens) the focal point of the lens. ¨ The focal point on the incident-light side is the near focal point; the focal point on the other side is the far focal point. ¨ The focal length � of the lens is the distance of the focal point from the lens. 18.5 Converging lenses ¨ A thin lens is an idealized lens whose thickness is zero and that lies entirely in a plane called the lens plane. ¨ Within the thin-lens approximation, all refraction occurs as the rays cross the lens plane, and all distances are measured from the lens plane. ¨ The special rays for a converging lens: Quiz: 18.5-2 through 18.5-4 18.5 Magnification ¨ The magnification � describes the orientation and size of the image relative to the object and its size. �" � = − � *+ ¤ � = is the ratio of image height to object height. * ¤ If � > 0, the image is upright relative to the object. ¤ If � < 0, the image is inverted relative to the object. 18.5 Virtual images ¨ When the object is inside the focal point of a converging lens, the refracted rays do not converge. ¨ Rays appear to diverge from a virtual image. ¨ Because no rays actually pass through a virtual image, placing a screen at the image plane would not produce an image. ¨ We use a sign convention defining the image distance �" to be negative for a virtual image. 18.5 Diverging lenses ¨ The special rays for a diverging lens: Quiz: 18.5-5 through 18.5-7.