Refraction, Lenses, & Color

Refraction The bending of light when it enters a different medium at an angle due to a change in speed. Light slows down and bends toward the normal when entering a more optically dense medium (greater n). Light speeds up and bends away from the normal when entering a less optically dense medium (smaller n). Air (n = 1.00) Glass (n=1.50) Glass (n=1.50) Air (n = 1.00)

Snell’s Law normal incident ray Air (ni =1.00) i n = index of refraction for the medium Boundary refracted ray r Water (nr = 1.33) Angles are always measured from the normal, never the surface

ni = index of refraction of incident medium θi = angle of incidence, degrees nr = index of refraction of refracting medium θi = angle of refraction, degrees

Index of Refraction Light changes speed (v) as it enters a new medium In a vacuum the speed of light (c) is 3.0 x 108m/s The index of refraction (n) of a material is the ratio of the speed of light in a vacuum to the speed of light in the material. Index of refraction has no units!

Critical Angle The angle of incidence that causes the angle of refraction to be 90o The refracted ray is tangent to the boundary between mediums Only possible when going from a more optically dense (high index of refraction) to less optically dense medium (low index of refraction) ni > nr c r=900 n=1 n=1.5

Critical Angle  

Total Internal Reflection When the angle of incidence exceeds the critical angle, the light does not cross the boundary into the new medium or refract. All of the light is reflected back into the incident (denser) medium according to the Law of Reflection (angle of incidence = angle of reflection) Application – fiber optic cables

Total Internal Reflection Angle of incidence > critical angle and ni > nr Angle of incidence = Angle of reflection      

Prisms Makes white light split up or disperse into the color spectrum The index of refraction depends on the wavelength of light so different colors of light bend or refract at different angles.

Dispersion The process of separating white light into its component wavelengths (or colors). As wavelength decreases, the index of refraction increases. Blue light refracts more than red light since it has a shorter wavelength and thus a larger index of refraction.

Diffraction The spreading out of light or other waves in the region behind an obstruction as they go around it or as they go between two obstructions.

Concave Lenses Thicker at the edges than in the center Parallel rays of light from a far object will refract through the lens and diverge as if they came from the focal point in front. Concave lenses are also called “diverging lenses”. Light may come in from either side of lens so there will be a focal point on both sides equal distances from the lens (assuming symmetrical lenses).

Convex Lenses Thicker in the center than at the edges Parallel rays of light from a far object will refract through the lens and converge at the focal point on the other side of the lens. Convex lenses are “converging lenses”. Light may come in from either side of lens so there will be a focal point on both sides equal distances from the lens (assuming symmetrical lenses).

Calculations f = focal length do = object distance di = image distance hi = image height ho = object height M = magnification

Interpreting Calculations Focal length (f) convex or converging lens, f = + concave or diverging lens, f = - Image distance (di) di=+ , image is real & on opposite side of object di= -, image is virtual & on same side as object Magnification (M) M & hi = +, image is upright M & hi = - , image is inverted

Ray Diagram Convex Lens (do>f) Image is real & inverted Draw 2 - 3 rays from tip of object: 1) parallel, then through primary f 2) through the center of the lens 3) through the front f, then parallel 4) Image is located where the refracted rays converge Image is real & inverted object f image f ’

Ray Diagram Convex Lens (Inside f) Image is virtual, Upright, & larger Draw 2-3 rays from tip of object: 1) parallel, then through primary f 2) through the center of the lens 3) from f on same side through tip of the object, then parallel 4) Extend the refracted rays back (dashed lines) to locate the image Ray Diagram Convex Lens (Inside f) image Image is virtual, Upright, & larger f f ‘ object

Ray Diagram Concave Lens Image is virtual, upright, & smaller Draw 2-3 rays from tip of object & refract at vertical line: 1) parallel, then refracted ray from f on same side of lens 2) through the center of lens 3) to lens along a line that would pass through f on the other side of lens, then parallel 4) Extend refracted rays back (dashed lines) to locate image object image f f Image is virtual, upright, & smaller

Polarizing filters Only allows light to pass through in one plane Light is reduced by one-half Sunglasses – polarized vertically, cuts out the horizontal components of light to reduce glare from horizontal surfaces such as sand or water

Photoelectric Effect When light of certain frequencies shine on a surface, electrons are emitted from the surface. Accounted for by the photon or particle theory of light. Many applications such solar panels, photomultiplier tubes (or PMTs used in high energy physics to study particle collisions), and photocells (which operate switches or relays for automatic door openers and burgular alarms).

Light and Color There are 3 primary colors of light RED, GREEN, & BLUE When these colors of light are mixed… White Light is produced This process is called color addition

Color Addition (Light) Red + Green = Yellow Red + Blue = Magenta Blue + Green = Cyan Red + Green + Blue = White Yellow, Magenta, and Cyan are called the secondary colors of light because they are produced using 2 of the primary colors.

Pigments Pigments work on the principle of color subtraction. The light we see is reflected light. A pigment of a certain color will reflect only that color of light and absorb all other frequencies. Example: A blue shirt will reflect incident blue light and absorb red and green.

Primary Pigments The primary pigment colors are magenta, cyan, and yellow because they absorb only one frequency of color. Yellow absorbs blue and reflects red and green. Cyan absorbs red and reflects blue and green. Magenta absorbs green and reflects red and blue.

Color Subtraction (Pigments) Mixing pigments means that you will see only the color that both colors reflect, others are absorbed. Red, Blue and Green are secondary pigments because they absorb 2 colors and reflect one. Magenta + Yellow = Red Cyan + Magenta = Blue Yellow + Cyan = Green

Complementary Colors Yellow & Blue Cyan & Red Magenta & Green Complementary colors are the same for light & pigment. For light, complementary colors combine to make white. For pigment, complementary colors combine to make black.

Black and White White light is the mixture of all colors (frequencies) of light. A white surface will reflect all colors of light. Black is not a color! Black is the absence of any reflected light. A black surface will absorb all incident light and reflect none.