VISUAL PHYSICS ONLINE WAVES: RAY MODEL OF LIGHT IMAGE FORMATION: THIN LENSES

The most important simple optical device is no doubt is the thin lens. Lenses are used in eyeglasses, camera, telescopes, microscopes, binoculars, and many specialized optical instruments. Fig. 1. Optical devises using lenses. Eyeglasses have been used since the late 1200s. The earliest known working telescopes appeared in 1608 in the Netherlands and are credited to Hans Lippershey. Galileo Galilei (the father of astronomy 1564 - 1642) on 7^th January 1610 made a discovery that shook the world and changed mankind's view of our place in the universe. On that evening, about an hour after sunset, Galileo pointed his home-built telescope towards Jupiter, and saw a peculiar sight: two tiny "stars" to the east of Jupiter, and one to the west, all arranged in a tight straight line along the ecliptic path with Jupiter itself. The next evening, almost on a whim, Galileo decided to check Jupiter again just to verify that the three "fixed stars" lay to the east of Jupiter, since he knew that the planet was moving westward against the background stars. Sure enough, there were the three stars again ... but on the west side of Jupiter, not its east! The only explanation was that those stars weren't "fixed" at all, but moved with Jupiter and indeed, seemed to move around it like our own Moon moves around Earth. This was the beginning of the end of the Aristotelian geocentric universe. A thin lens is usually circular in cross-section and has two faces which are portions of spherical surfaces. Lenses can be classified as converging or diverging (figure 2). The two faces of thin lenses can be any combination of convex, plane or concave shaped surfaces. The important property of lenses is that they form images of objects. Fig. 2. Different types of converging and diverging lenses. CONVERGING THIN LENSES A converging lens can be used to focus a parallel beam of light on to a spot on the focal plane called a focal (focus) point as shown in figure 12. The distance from the axis of the lens to the focal plane is called the focal length f of the lens. Fig. 3. Rays parallel to the optical axis are focused at a point called the principle focus or principle focal point. Other sets of parallel rays are bought to a focus along the focal plane. N.B. The ray through the centre of the lens does not deviate. It is easy to find the location of an image of an object for a converging lens using a ray tracing diagram. Select two points on the object the top and bottom. Only two rays are necessary from each point to give the image location, but the three most useful rays often used are: 1. A ray drawn parallel to the optical axis from the object will be deviated by the lens so it passes through the principle focal point in the focal plane. 2. A ray drawn from the object passing through the centre of the lens has zero deviation. 3. A ray drawn from the object through the principle focal point on the object side of the lens will emerge from the lens parallel to the optical axis. The intersection of these three lines in the object plane will determine the location and characteristics of the image. The lens equation for thin lenses relates the focal length to the object distance and the image distance (2) lens equation (thin lens) If the height of the object is and the height of the image is , the lateral magnification is (3) Sign Conventions Converging lens Diverging lens Object on side of lens light is coming from Image on the opposite of the lens from where the light is coming Image on the same of the lens from where the light is coming Object upright Image upright Image inverted Figure 4 show the three rays drawn from the object (tree) to locate the position of the image from the top and from the bottom of the object. The measurements for distances from figure 4 are: From the lens equation (equation 2) the predicted image distance is The lateral magnification (equation 3) image is inverted The predicted height of the image (equation 3) is image is inverted Fig. 4. Ray tracing can be used to estimate the location of the image of an object. Object placed within the focal length of the lens Fig. 5. Simple magnifying glass - object placed within the focal length of a converging lens produces a virtual, upright and magnified image. virtual image upright image image height greater than object height Object placed at the focus of the lens Fig. 6. Object placed in the focal plane. The virtual image is at infinity. virtual image at infinity upright image and infinite in height Object placed at the focus of the lens Fig. 7. The object distance is equal to than twice the focal length . The image is real, inverted and same height as object, magnification . real image inverted mage image height equal to object height Object at Fig. 8. The object distance is greater than twice the focal length . The image is real, inverted and reduced in height, magnification . real image inverted mage image height less than to object height

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Ian Cooper School of Physics University of Sydney

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