Pre AP Physics Light & Optics Chapters 14-16 Light is an electromagnetic wave Electromagnetic waves: Oscillating electric and magnetic fields that are perpendicular to the direction the wave moves Difference frequencies & wavelengths o In visible light, this gives different colors Electromagnetic spectrum (in order of increasing frequency & decreasing wavelength) Radio waves Microwaves Infrared waves Visible Light (ROYGBIV) Ultraviolet light X rays Gamma rays All forms of EM waves travel at the speed of light in a vacuum = 3.00 x 10 8 m/s This speed is constant in air as well c = f λ (velocity of a wave formula, but speed of light is special and gets its own variable c) Brightness of light decreases by the square of the distance from the source because the light is spreading out If move 2x s away from source, the brightness decreases by 4 Light traveling through a uniform substance (medium) always travels in a straight line If it encounters a different medium (at a boundary), its path will change If the new medium is opaque, some light is absorbed & some is reflected a good mirror can reflect 90% of incident light Texture of surface affects reflection If a rough, textured surface, light is reflected in many different directions diffuse reflection Ex. Paper, cloth, unpolished wood
If smooth, shiny surface, light is reflected in one direction only specular reflection Ex. Mirror, water in a pond Incoming & reflected angles are equal (law of reflection) Mirrors 3 types of mirrors flat/plane, concave & convex Flat/Plane mirrors Simplest of all mirrors If an object is placed in front of flat mirror & light is bounced off object, the light rays spread out from the object and reflect from the mirror s surface To the observer, the rays appear to come from a location on the other side of the mirror when this happens, the image is called a virtual image A flat mirror always forms a virtual image which can only be seen behind the surface of the mirror Image formed by a flat mirror has right to left reversal right side of the object is the image s left side Distance of object to mirror (s o ) = distance of image to mirror (s i ) Height of object (h o ) = height of image (h i )
Curved Mirrors Concave & Convex Concave Mirrors: - used when need a magnified image (dressing table, dentist) - also called converging mirror because light rays converge after reflection - amount mirror is curved determines 1) where image will appear & 2) how large the image will be - Radius of curvature (R) is the distance from the mirror s surface to the center of curvature (C) of the sphere that the mirror is a small part of - The focal point (F) occurs at the ½ way point between the mirror & the center of curvature the focal length (f) is the distance from the mirror to the focal point - Can form real image an image that can be displayed on a surface - Can also form a virtual image image that appears behind the mirror Mirror Equation Relates object distance, image distance & focal length 1/s o + 1/s i = 1/f s o = object distance s i = image distance f = focal length Can also calculate Magnification how large or small image is with respect to the object s size, is unitless (because a ratio) M = h i /h o = - s i /s o Sign Convention for mirrors Image distance: Real images occur on side of mirror in which light rays reflect (front side of mirror) s i is + Virtual images occur on side of mirror where no light rays reflect (back side of mirror) s i is (-) Heights (objects & images) h is + when is above principal axis (upright) h is (-) when is below principal axis (inverted) Focal length (f) f is + when converging (concave mirror) f is (-) when diverging (convex mirror)
Magnification M>1 = image larger than object M<1 = image smaller than object Ray Diagrams used to locate an image formed by a mirror - Draw to scale - Can draw 3 reference rays only need 2 to see where image is formed (image is formed where two lines intersect) From Object to Mirror From Mirror after reflection 1. parallel to principal axis through focal point (F) 2. through focal point (F) parallel to principal axis 3. through center of curvature (C) back along itself through C RAY DIAGRAM WS As move object relative to mirror image changes a. if the object is further from mirror than the focal length image is real & inverted b. if the object is at the focal point image is not formed c. if the object is between F & mirror image is virtual & upright [Mirrors WS #1-6] Convex mirrors - image smaller than object - images distorted near the edges - also called a diverging mirror because rays diverge after reflection - focal point & center of curvature on opposite side of mirror (behind the mirror) so focal length is negative - image always virtual (image distance always negative) - Applications: Take objects in a large field of view & produce a small image which gives observer a complete view of a large area in stores to help monitor customers, intersections of busy hallways, passenger s side mirror in car ( objects are closer than they appear ) Ray Diagrams use same rays as concave mirror, except when rays extend behind mirror, they are drawn as dotted lines since the light rays don t actually travel there Focal point & center of curvature is behind mirror RAY DIAGRAM WS Images are always virtual, upright & reduced [Mirrors WS #7-10]
Refraction - Bending of light as it travels from 1 medium to another - When light travels from one transparent medium to another at any angle other than straight on (parallel to normal), light ray changes direction when it meets the boundary Angles of incoming (incident) light rays & refracted light rays are measured with respect to the normal (a dotted line drawn perpendicular to the boundary) Angle between the incident ray & normal is the angle of incidence Θ i Angle between the refracted ray and normal is the angle of refraction Θ r Speed of light changes when it is traveling through different materials (glass, water, ice, diamonds, quartz) When light moves form a medium where speed is faster to medium where speed is slower ray bends TOWARD normal Ex. Air glass If light moves from medium with slower speed to medium with faster speed ray bends AWAY from normal Ex. Glass air If incident ray is parallel to normal (perpendicular to the boundary), no refraction occurs The path of a light ray that crosses a boundary is reversible Law of Refraction (Simulation)
Index of refraction (n) ratio of speed of light in a vacuum (air) to the speed of light in a medium - always greater than 1 - air = 1 (which is smallest index of refraction) n = c/v n = index of refraction (ration therefore no units) c = speed of light in vacuum (or air) (3 x 10 8 m/s) v = speed of light in medium What happens to the index of refraction if v gets faster? Slower? The larger the index of refraction, the slower light travels through the medium, & the more the light ray will bend when it passes into the medium from a vacuum/air Objects appear to be in different positions due to refraction Ex. Cat on a pier looking at fish underwater - cat perceives fish to be closer to surface - fish perceives cat to be further away
Index of refraction is affected by wavelength When white light passes through a prism & separated into the colors (ROYGBIV), each color refracts a different amount since each color of light has a different wavelength To find angle of refraction, use Snell s Law: n 1 sinθ 1 = n 2 sinθ 2 [WS #11-14] Light traveling through a pane of glass is bent towards normal when enters pane As it exits, light is bent again & since speed increases, is bent away from normal It leaves the pane of glass traveling parallel to the ray that entered the glass The sideways displacement depends on 1. thickness of pane 2. index of refraction 3. angle of incidence of light ray Lenses Like mirrors, can form images but by refraction instead of reflection Images can be real or virtual depending on the type of lens & placement of object Used in optical instruments microscopes, cameras, telescopes, your eye 2 main types converging & diverging Focal point can occur on either side of the lens since light can pass through either way (unlike mirrors) Converging lens focal point on opposite side of where object is placed - can produce real or virtual images
Diverging lens focal point on same side as where object is placed F occurs where diverging rays appear to originate - only produce virtual, upright, reduced images - Thin Lens Equation (same as mirror equation) (applies to lenses that are thinner than their focal length) 1/s o + 1/s i = 1/f s o = object distance s i = image distance f = focal length Can also calculate Magnification how large or small image is with respect to the object s size, is unitless (because a ratio) M = h i /h o = - s i /s o Sign Convention for lenses Image distance: Real images occur on side of mirror in which light rays reflect (front side of mirror) s i is + Virtual images occur on side of mirror where no light rays reflect (back side of mirror) s i is (-) Heights (objects & images) h is + when is above principal axis (upright) h is (-) when is below principal axis (inverted) Focal length (f) f is + when converging f is (-) when diverging Magnification M>1 = image larger than object M<1 = image smaller than object
Ray Diagrams 3 rays can draw: From object to lens From lens refracted 1. parallel to principal axis passes through focal point (F) 2. to center of lens from center of lens 3. passes through focal point or parallel to principal axis Back toward focal point Eye is like a lens if have systems with more than 1 lens, calculate image of 1 st lens normally (ignoring second lens) & then use image of lens 1 as object of lens 2 to get final image Magnification is calculated for the system by multiplying the magnifications of the separate lenses Exs. Compound microscopes = 2 converging lenses Refracting telescopes = 2 converging lenses Polarization of Light Waves In electromagnetic wave, electric field is at right angles to the magnetic field & direction of propagation (3D) Light from typical source consists of waves with electric fields oscillating in random directions unpolarized light It is possible to separate waved with vertical oscillations from waves with horizontal oscillation linear polarization Linear polarization can occur 2 ways 1. Linear polarization by transmission - send light through certain transparent crystals - direction of polarization is determined by arrangement of atoms/molecules in crystal - effect is similar to sending transverse waves along a rope through slats of a picket fence & only transverse waves in up & down direction can pass through while all others are blocked - transmission axis = line along which light is polarized when polarized by transmission - only light waves that are linearly polarized with respect to transmission axis can freely pass through Can use a polarizing substance to determine if & how light is linearly polarized by rotating substance as beam of polarized light passes through, will see a change in intensity of light - light is brightest when plan of polarization is parallel to transmission axis - when transmission axis is perpendicular to plane of polarization of light, no light passes through
2. Polarization by reflection - when light is reflected at certain angles from a surface, reflected light is completely polarized parallel to reflecting surface - if surface is parallel to ground, light is polarized horizontally - ex. Glaring light reflected at low angle from roads, bodies of water 7 car hoods - because light that causes glare is usually polarized horizontally, can be filtered out by a polarizing substance with vertical transmission axis i.e. polarizing sunglasses Rainbows can be observed anytime observer is between source of light & water droplets in air - sunlight strikes the water droplets & passes through front surface, it is then partially reflected back to the observer from the back of the droplet - rainbow occurs because sunlight is bent as it passes from air to water and then back from water into air Color (USE DEMOS!!!) Have you ever noticed that the color of an object can appear different when placed in different lighting conditions? This occurs because of differences in the light reflecting & absorbing properties of the object being illuminated Color of an object depends on which wavelengths of light shine on the object & which wavelengths are reflected The color an object appears is the color/wavelength that is reflected i.e. a green leaf in white light reflects green wavelengths and absorbs all others White = all colors reflected Black = all colors absorbed & none reflected If green leaf in red light leaf appears black because no green to reflect, just red that gets absorbed Prisms can disperse white light into its elementary colors (ROYGIV) sending the elementary colors back through a prism combines them into white light Additive Primary Colors Red, Green, Blue - when added in varying proportions, can form all the colors of the spectrum - Red & green combine to form yellow which is a complimentary color of blue since when yellow & blue are combined it forms white light - 2 primary colors combine to produce the complement of the 3 rd primary color
Applications of additive primary colors - certain chemical compounds give color to glass ex. Iron green Manganese magenta Since green & magenta are complementary colors the right proportions will give clear glass - color TV screen consists of small, luminous dots (pixels) that glow either blue, green or red. By varying brightness of the different pixels can produce many different colors Subtractive primary colors cyan, magenta, yellow - pigments (paints or crayons) - when pigments are mixed, each one subtracts certain colors from white light and the resulting color depends on the frequencies NOT absorbed - when 2 primary subtractive colors are combined they produce either red, green or blue pigments - When 3 primary pigments combined in proper proportion, makes black