Our everyday experience that light travels in straight lines is the basis of the ray model of light. Ray optics apply to a variety of situations, including mirrors, lenses, and shiny spoons. Chapter Goal: To understand and apply the ray model of light. 1/28/09 1Topics: • Reflection • Refraction • Image Formation by Refraction • Thin Lenses 1/28/09 2Huygen’s Principle: • Each portion of an advancing wave acts as a synchronous source. • Aperture size ~wavelength=>diffraction • Aperture size>>wavelength=>ray model works well 1/28/09 3Ray model: • Each point of an object emits rectilinear rays in all directions 1/28/09 4 Diffraction model: • The energy represented by each ray is actually spread out a bit. Ignore that in ray model.1/28/09 5 Atoms emit, absorb, and scatter light waves. The response to incident light depends sensitively on wavelength and type of atom. For visible wavelengths, air is quite transparent (not absorbing, water droplets do scatter), glass, water, and lucite plastic are fairly transparent, metals are opaque but reactive/reflective. The speed of light depends on the medium v=c/n where c =vacuum speed = 3e8 m/s, n=“refractive index” = 1 (gas) to 1.5ish (water)1/28/09 6 • Ray incident • Ray reflected • Ray refracted • Ray reflected • Ray refracted An interface between materials produces reflection and oblique transmission (refraction) Note also diffuse random scattering and absorption.Reflection and refraction: Huygen’s picture 1/28/09 7 n1 n2>n1 v2<v1 Refraction angle depends on change in wave speed. v1 Law of reflection Law of refractionA glass stirring rod (n=1.46) is dipped into beaker of Wesson oil (n=1.46). What happens to the appearance of the rod? Pyrex stirring rod A. Appears dark B. Appears bright C. Appears invisible D. Appears curved E. Appears inverted Hint: No reflection/refraction if index of refraction is same. Beaker of Wesson oil What do you think?1/28/09 9 Light speed and the refractive index depend on frequency/wavelength/color as does refraction angle. A piece of glass separates/ disperses the colors in mixed light.1/28/09 10 Total Internal Reflection • When light is directed from n1 > n2 transmission weakens and vanishes as the refraction angle exceeds 90 degrees. • Critical angle: angle of incidence that will result in an angle of refraction of 90° For water: sinθc=11.333= 0.75 ⇒θc= 48.75˚Optical fiber light guide applications 1/28/09 11 The cladding n lower n than the core – Telecommunications signals piped by internal reflection on fiber channels – Endoscope transport of optical images from the interior of a body.Imaging with a pinhole camera 1/28/09 12 We live in a confusing bath of unfocused light. A pin hole selects and channels light creating a real image (albeit inverted) – the illumination at each point on the image plane is a sample of a point on the object. Object Image A real image occurs for any s’. s’ sMore on the pinhole camera 1/28/09 13 Try it: Remove contacts/glasses. Make pin hole with thumbs and index fingers and compare focus of distant small light source. Limitations: As the pinhole diameter decreases, the image becomes increasingly sharp until diffraction is important but the light intensity decreases as the square of the diameter. Great for imaging a solar eclipse on a piece of paper that can be viewed. (Don’t ever look directly at an eclipse!)Imaging with a refracting lens 1/28/09 14 Object Image Image is formed at distance s’ determined by object distance s and the strength (focal length f) of the lens.More on the refracting lens 1/28/09 15 The lens collects light over its entire diameter typically larger than a pinhole=> bright image. Problems: Spherical surfaces produce exactly focus only rays near the axis. The refractive index and focal length depend on wavelength so different colors are focused to different planes (chromatic aberration)The human refracting lens 1/28/09 16 Lens (adjustable strength!)!Object!Image!1/28/09 17 Imaging with a mirror A real image can be formed by a convex mirror. The focal length is half the radius of curvature. The mirror version of the thin lens equation applies. Example: plane mirror: R is infinite, f is infinite, s’=-s is negative, the image is virtual – the light is that which would be generated by a source at the location of the virtual image.Applications 1/28/09 18Applications 1/28/09 19A paraxial ray A. moves in a parabolic path. B. is a ray that has been reflected from parabolic mirror. C. is a ray that moves nearly parallel to the optical axis. D. is a ray that moves exactly parallel to the optical axis. 1/28/09 20A paraxial ray A. moves in a parabolic path. B. is a ray that has been reflected from parabolic mirror. C. is a ray that moves nearly parallel to the optical axis. D. is a ray that moves exactly parallel to the optical axis. 1/28/09 21The focal length of a converging lens is A. the distance at which an image is formed. B. the distance at which an object must be placed to form an image. C. the distance at which parallel light rays are focused. D. the distance from the front surface to the back surface. 1/28/09 22The focal length of a converging lens is A. the distance at which an image is formed. B. the distance at which an object must be placed to form an image. C. the distance at which parallel light rays are focused. D. the distance from the front surface to the back surface. 1/28/09 23Lateral Magnification The image can be either larger or smaller than the object, depending on the location and focal length of the lens. The lateral magnification m is defined as 1. A positive value of m indicates that the image is upright relative to the object. A negative value of m indicates that the image is inverted relative to the object. 2. The absolute value of m gives the size ratio of the image and object: h'/h = |m| . 1/28/09 24EXAMPLE 23.15 Designing a lens 1/28/09 25 Something small can be made to appear bigger. Wow!EXAMPLE 23.15 Designing a lens 1/28/09 26Closing thoughts 1/28/09 27 So many questions are raised by this introduction. How do we make light? How do we detect light? How small a thing can we see? Gradually we may answer these questions. Physics is a tapestry. You pull on a thread and it leads to others. In this course we
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