Light, Reflection, and Refraction Chapters 14 and 15

Electromagnetic Waves An electromagnetic wave is composed of a magnetic field wave perpendicular to an electric field wave All objects that are not at absolute zero emit EMWs. The hotter the object the more waves they emit. The electromagnetic spectrum is composed of a range of wavelengths and frequencies that range from radio waves to gamma waves. Visible light is a very small portion of that entire spectrum.

c The speed of an electromagnetic wave in a vacuum is 3.00 x 10 8 m/s. It is equal to the product of the wavelength and the frequency c = ƒ Sample Problem 14A

Visible Light Visible Light is the part of the EMS that we can see Ranges from the color red with a wavelength of 700nm (x10 -9 m) to the color purple with a wavelength of 400nm.

Reflection Light waves usually travel in straight paths. When a light wave encounters a different substance it changes direction. When it encounters a substance that does not permit light to travel through it, opaque, some of the light will be reflected. Usually a portion of the light is absorbed.

Reflection (cont) The texture of the opaque object’s surface affects how it reflects light. A rough object reflects light in many different directions, diffuse reflection A smooth object reflects light in only one direction, specular reflection A surface is considered smooth if variations are smaller than the size of the wavelengths being reflected. It is difficult to make objects smooth enough to reflect X-rays and Gamma Rays.

Mirrors Mirrors are smooth surfaces that reflect nearly all of the light they encounter. Light that strikes a mirror at an angle from the normal line reflects at the same angle away from the normal line

Flat Mirrors Flat mirrors are the simplest form of mirror where the objects distance to the mirror, p, is equal to the distance from the mirror to the image, q. The image appears to be located behind the mirror and is considered to be a virtual image as the object would not appear on a screen.

Ray Diagrams Ray diagrams are used to predict the location of the image of an object. To make a ray diagram for a flat mirror choose a point on the object and draw a ray toward the mirror at a perpendicular angle. This ray would reflect back on itself. Then draw a ray at an angle toward the mirror and draw the reflection of that ray. Trace back both of the reflected rays through the mirror, where they intersect, place the image.

Concave Spherical Mirrors Concave spherical mirrors are those who reflective surface is on the interior of a curved surface that has a radius R to the center of curvature C. The optical axis is any line that passes through C and is usually oriented with an object.

Concave Spherical Mirror Rules A ray traveling through C will reflect back through C. (only if object is beyond C) A ray traveling through the focal point f, halfway between C and the surface of the mirror, will reflect parallel to the OA A ray traveling to the intersection of the OA and the mirror will reflect at the same angle below the OA. A ray traveling parallel to OA will reflect through the focal point

Ray Diagrams Using any of the two rules you must draw two rays, the object occurs at the point of intersection. We will draw several ray diagrams to determine the image produced by an object that is –Beyond C –Between C and f –Between f and mirror

Convex Spherical Mirrors Convex spherical mirrors are those where the reflective surface is on the outside of the curve. The points f and C are located behind the mirror Convex spherical mirrors have rules as well.

Rules A ray parallel to the OA will reflect directly away from f. A ray heading towards f will reflect parallel to the OA A ray heading towards C will reflect directly away from C. A ray heading toward intersection of OA and mirror will reflect at the same angle below the OA. Trace the 3 diverging lines back through the mirror to reveal the location of the image which is always virtual

Equations While ray tracing gives us a good idea of the location of an object it is always best to verify with math. If p is the object’s distance and q is the image distance then… 1/p + 1/q = 1/f The magnification of the object can been calculated using the equation… M = -(p/q) Sample Problem 14C

Parabolic Mirrors Rays that hit spherical mirrors far away from the OA often reflect though other points causing fuzzy images, spherical aberration. Telescopes use parabolic mirrors as they ALWAYS focus the rays to a single point.

Refraction Substances that are transparent or translucent allow light to pass though them. When light passes from one transparent/translucent substance to another it changes direction. This change is due to the slight differences in speed that light travels in the new substance. This is called refraction.

Analogy A good analogy for refracting light is a lawnmower traveling from the sidewalk onto grass.

Index of Refraction The ratio of the speed of light in a vacuum to the speed of light in a medium is that medium’s index of refraction. (n) The higher the index of refraction, the slower light travels through a medium. Refraction causes objects to appear at locations they are not at.

Snell’s Law Snell’s Law relates the indices of refraction as well as the angle away from the normal line (angle of incidence) to determine the angle of refraction. n 1 (sin  i ) = n 2 (sin  r )  r = sin -1 {(n 1/ n 2 )(sin  i )} Sample Problem 15A

Total Internal Reflection If the angle of incidence of a ray is very large(close to 90º) the ray will reflect rather than refract. This principal is responsible for the properties of fiber optic cables. Remember the lawn mower analogy…

Thin Lenses Refraction is the property that allows us to manipulate an object’s image using a lens. We will be working with converging and diverging lenses. Just like with mirrors, we will need to follow rules to draw ray diagrams to predict the location of an image. Thin lenses also have focal points, these points are determined not only by the curve of the lens but the index of refraction of the lens as well. A lens has two focal points, one on either side.

Converging Lens Diagram Draw one ray parallel to OA, refracts through focal point. Draw one ray through center of lens, continues straight through. Draw one ray through focal point, refracts through lens, travels parallel to OA. Image located at intersection of rays. Treat lens as though it were a flat plane.

Diverging Lens Diagram Because the rays that enter a diverging lens do not intersect a virtual image is formed by tracing back the refracted rays. Ray 1 - parallel to OA, refracts away from f, trace back to f. Ray 2 - ray toward f, refracts parallel to OA, trace back parallel to OA Ray 3 - ray through center, continues straight, trace back toward object

Equations You can use the same equations for curved mirrors with lenses If p is the objects distance and q is the image distance then… 1/p + 1/q = 1/f The magnification of the object can been calculated using the equation… M = -(p/q) Sample problem 15B