Convex lenses
...concave lenses produce only small virtual images. 66. At the critical angle a wave will be refracted to 90 degrees. 67. Total internal reflection occurs at angles greater than the critical angle. 68. Light rays bend away from the normal as they gain speed and a longer wavelength by entering a slower index of refraction (less optical density) medium while the frequency remains constant. 69. Light slows down, bends toward the normal and has a shorter wavelength when it enters a higher index of refraction (high optical density) medium while the frequency remains constant. LIGHT What is light? rays, particles, waves. For this lecture, think of light as being made up of many infinitely small particles, called "photons" or "quanta", emitted by excited atoms (e.g., in the Sun, or a light bulb, or a lighter.) Each photon is characterized by two numbers: a polarization angle (not important for vision) and a wavelength (very important for vision: wavelength determines perceived color.) Wavelength range = 400 nanometers (nm) = deep blue up to 700 nm (deep red). Green = about 550 nm. Yellow = about 570 nm. photons travel (fast!) in straight-line paths (path= "ray") until a new medium is encountered. Then: the photon is either absorbed, or reflected, or refracted: *Absorbtion: the photon is absorbed by an atom in the new medium. *Reflection: the photon bounces off an atom in the new medium. *Refraction: photon passes on into the new medium, but usually its direction is changed (the ray is bent). The amount of bending is determined by the relative speeds of light in the old and new media. Snell's law: sin (angle of refraction ) speed in new ----------------------------------------- = ---------------------- sin (angle of incidence) speed in old One implication: if the two speeds are the same, there is no bending (e.g. water and cornea). Chromatic aberration : in materials, the shorter the wavelength, the slower the light. Hence, shorter wavelengths are bent more than longer ones. This is why a prism breaks up white light into a rainbow. SOME FACTS ABOUT LENSES CONVEX LENSES look like this : When a convex lens casts an image of an object onto a screen, the image is inverted (upside down). And its location in space depends on the distance between the object and the lens. When you look thru a convex lens, distant objects appear inverted and reduced, while near objects appear erect and enlarged. CONCAVE LENSES look like this:  Concave lenses can't cast images onto screens. When you look thru a concave lens, both near and far objects appear erect and small. Light Image formation - the image of a point source. Photons travel out in all directions from a point. Those that pass thru a lens are refracted so that after leaving the lens all the photons are heading for some common destination. That destination is the IMAGE of the point - if we put a screen there, we see a point on the screen (a sharply focused image of the point source). If the screen is placed too close to the lens, or too far from it, the image of the point will be blurred ("out of focus").  Refractive errors of the eye. MYOPIA : eye too long. HYPEROPIA: eye too short. NOTE: the situation is the same if the point is reflecting light rather than emitting it.  Images of extended objects: think of the object as just a collection of points, each forming its own image.  The NODAL POINT = a point in the center of a lens such that : rays entering the lens headed towards the NP are not bent as they pass thru the lens. We use this fact to determine where the image of any point will appear on a screen. TYPES OF LENSES (CONVEX AND CONCAVE) AND TYPES OF IMAGES (REAL AND VIRTUAL) Convex lenses (fatter in center than at the rim) can form both real and virtual images. Object distance and image distance : when an object is "infinitely" distant from a convex lens, its image is formed at the FOCAL LENGTH of that lens. As the object moves closer to the lens, its image moves farther from the lens. When the object reaches a distance of one focal length, its image is located "at infinity" on the far side of the lens. If the object moves closer than a focal length, it no longer forms a real image. Instead, its image becomes VIRTUAL.  DIOPTER VALUE = 1/ focal length in meters. Seeing A "Real" Image  Seeing A "Virtual" Image  In 1608, a Dutch eyeglass maker named Hans Lippershey looked at a church steeple through two lenses placed one in front of the other and saw that the image was magnified. Unfortunately the telescopes built on Lippershey's model had poor image quality, caused by the bending of light though the glass lenses. (Glass does not bend the different colors of light equally. Red light is bent the least causing a colour distortion in the image.) Isaac Newton eventually solved this problem in 1668 by making a telescope that worked with mirrors instead of lenses. Galileo Galilei was the first person to use the telescope to seriously study the heavens. Galileo was able to see that the moon was not smooth, but covered with huge valleys and craters. He discovered four moons orbiting Jupiter and found out that Venus has phases just like the moon. He realized that this must mean that Venus, and the other planets, revolve around the sun not around the earth, as many people believed at the time. In 1610 Galileo published a book about what he had seen through his telescope. Starry Messenger became the seventeenth-century equivalent of a bestseller. Not bad! Telescopes make it possible for astronomers, and us, to study the universe. Pretend we are outside one evening with our telescope looking at a planet, say Venus. (We are definitely ...