Chapter 14 Light and Reflection

14.1 Characteristics of Light Objectives Identify the components of the electromagnetic spectrum Calculate the frequency or wavelength of electromagnetic radiation Recognize that light has a finite speed Describe how the brightness of a light source is affected by distance

White Light What appears to us to be white light from a bulb or the sun is actually a spectrum of waves The visible spectrum can be separated into six primary colors: ROYGBV The invisible spectrum includes other forms of radiation (X-rays, microwaves, radio waves). Visible or invisible, they are all electromagnetic waves.

Electromagnetic Waves …are transverse waves consisting of oscillating electric and magnetic fields at right angles to each other.

Electromagnetic Waves, cont. Since the E-field and the B-field oscillate perpendicular to the direction of wave travel, electromagnetic waves are transverse waves All electromagnetic waves travel at the speed of light

Electromagnetic Wave Speed Equation for Wave Speed: c = f λ where: c = speed of light (m/s) f = frequency (Hz) or (1/s) λ = wavelength (m) c = 3.00 x 108 m/s

Question The AM radio band extends from 5.4x105 Hz to 1.7x106 Hz. What are the longest and shortest wavelengths in this frequency range? c = f λ, so λ = c / f Answers: Longest λ = 5.6x102 m Shortest λ = 1.8x102 m

Wave Trivia Why can radio waves travel through space but sound waves can’t? Hints: What kind of wave is a sound wave and what does is need in order to propagate?

Wave Trivia, cont. Why do you see lightening much sooner than you hear the thunder? Speed of Light 3.0x108 m/s Speed of Sound 343 m/s

Wave Trivia, cont. Can you get a sunburn on a cloudy day?

Waves Huygens’ Principle Wave fronts are lines of particles that represent a position within any given wave Wavelet is a spherical or secondary wave produced by point sources along the wave front Ray approximation is a simplification that treats the propagating wave as a straight line (ray) perpendicular to the wave front

Huygens’ Principle

Brightness Since light emits in all directions, the farther the light is you are from the source the more spread out the light will be. Therefore, the light appears less bright as you get farther away from the source Brightness decreases by the square of the distance from the source

14.2 Flat Mirrors Objectives Distinguish between specular and diffuse reflection of light Apply the law of reflection for flat mirrors Describe the nature of images formed by flat mirrors

Reflection …the turning back of an electromagnetic wave at the surface of a substance Most substances absorb at least some of the incoming light wave, and reflect the rest

Reflection, cont. Diffuse Reflection Specular Reflection The manner in which light is reflected from a surface depends on the surface’s smoothness Diffuse Reflection Specular Reflection

Reflection, cont. Angle of incidence is the angle between a ray that strikes s surface and the normal to the surface at that point Angle of reflection is the angle between the normal to the surface and the direction in which the reflected ray moves θ1 = θ2

Flat Mirrors If an object is placed a distance in front of a flat mirror, the image of the object will appear to be located behind the mirror

Flat Mirrors, cont. The object distance (p) in front of the mirror is equal to the image distance (q) behind the mirror The image formed by light rays that appear to intersect behind the mirror, but never really do, is called a virtual image

Ray Diagrams Draw the first ray perpendicular …use simple geometry to locate an image formed by a mirror Draw the first ray perpendicular to the mirror’s surface. Its angle of incidence and of reflection are both zero. Draw the 2nd ray at an angle that is not perpendicular to the mirror’s surface. The angle of incidence will equal the angle of reflection. Trace both reflected rays back to their image location behind the mirror.

Sources of Light (Worksheet Handout) Luminous bodies: emit light Illuminated bodies: reflect light Measurements of light are made by comparing light sources with the output of known luminous bodies.

Sources of Light, cont. The rate at which light is emitted from a source is called luminous flux. Luminous flux is denoted by the letter P, with units of lumens (lm). The amount of illumination a light source provides to an object depends on how far away from the object the light source is. The actual amount of illumination onto a surface is called illuminance. The symbol for illuminance is E, and units are lm/m2.

E = P / (4r2) Sources of Light, cont. Relationship between luminous flux (P) and illuminance (E): E = P / (4r2) This equation works only if the light source is small enough or far enough away to be considered a point source, and only if the surface is directly facing the light source.

I = P / (4) Sources of Light, cont. Another way to measure the output of a light source is in candelas. The symbol for candelas is I, and the units are cd. The relationship between luminous flux (P) and candelas (I) is: I = P / (4)

Sources of Light, final. Summary of terms: P: luminous flux (output of a light source) E: illuminance (the amount of light that hits a surface) I: candela (another measure of the output of a light source)

14.3 Curved Mirrors Objectives Calculate distances and focal lengths using the mirror equation for concave and convex spherical mirrors 2. Draw ray diagrams to find the image distance and magnification for concave and convex spherical mirrors 3. Distinguish between real and virtual images 4. Describe how parabolic mirrors differ from spherical mirrors

Concave Spherical Mirrors …an inwardly curved, mirrored surface that is a portion of a sphere and that converges incoming light rays Concave mirrors magnify the image Common use is a dressing table mirror

Image from a Concave Spherical Mirror Determined by The radius of curvature of the mirror (R), which is the same as the radius of a sphere whose center of curvature is (C) and whose curvature is the same as the mirror The distance the object is away from the mirror (p)

Real and Virtual Images Real images are formed if the light rays actually intersect at a single point. These images can be displayed on a surface, like the images on a movie screen. Virtual images are created when the light rays don’t really intersect, but appear to intersect. These images cannot be displayed on a surface.

Image Location 1/p + 1/q = 2/R Where: p is the object distance q is the image distance R is the radius of curvature

Image Location, cont. 1/p + 1/q = 2/R If the object distance (p) is far enough away from the mirror, then 1/p approaches zero, and the image distance (q) therefore approaches R/2. This means the image forms at a location halfway between the mirror and the center of curvature of the mirror (C). This location is called the focal point of the mirror, and is denoted by the letter F.

Focal Point When the image is located at the focal point, image distance is called the focal length (f).

1/p + 1/q = 1/f Mirror Equation Using the original equation and the new variable for focal length (f), the mirror equation becomes: 1/p + 1/q = 1/f p is object distance q is image distance f is the focal length, which is half the radius of curvature of the mirror

Center of curvature (C) and focal point (f) 1/p + 1/q = 2/R Where R is the radius of curvature for a spherical mirror whose center is located at C. 1/p + 1/q = 1/f R = 2f 2/R = 1/f or Since R=C, C is located twice as far from the mirror as f.

Mirror Equation Conventions Real images are formed on the front side of the mirror, where rays reflect Virtual images are formed on the back side of the mirror, where light rays do not really exist Mirrors are drawn so that the front side is to the left of the mirror Object and image distances are positive if they are on the front side of the mirror and the image distance is negative if it on the back side of the mirror Object and image heights are positive when they are above the principle axis, and negative when below

Magnification M = h’/h = - q/p Curved mirrors form images that are not the same size as the object Magnification is the measure of how much larger or smaller the image is compared to the object Equation for magnification (M): M = h’/h = - q/p h = object height q = image location h’ = image height p = object location

Concave Mirror Example A concave spherical mirror has a focal length of 10.0cm. An upright object is placed 30.0cm from the mirror. Where is the center of curvature (C) located? What is the image distance? What is the magnification? Is the image upright or inverted? Is the image real or virtual?

Magnification, cont. - + Sign conventions for magnification upright Orientation of image with respect to object Sign of M Type of image this applies to upright + virtual inverted - real

Ray Diagrams for Curved Mirrors …are used to check values calculated from mirror and magnification equations Similar to ray diagrams for flat mirrors, but use three reference rays instead of two Need to measure and locate center of curvature (C) and focal point (F) along the principle axis

Rules for Drawing Ray Diagrams Ray Number Line drawn from object to mirror Line drawn from mirror to image after reflection 1 parallel to principle axis through focal point f 2 3 through center of curvature C back along itself through C

Ray 1 Ray 2 Ray 3

Convex Spherical Mirrors …an outwardly curved mirrored surface that is a portion of a sphere that diverges incoming light rays The image is always virtual The image distance is always negative

Ray Diagram – Convex Mirror

Convex Mirror Example An upright object is placed 10.0cm from a convex spherical mirror with a focal length of 8.00cm. Where is the center of curvature (C) located? What is the image distance? What is the magnification? Is the image upright or inverted? Is the image real or virtual?

Spherical aberration occurs when parallel rays far from the principle axis converge away from the mirror’s focal point

Parabolic Mirrors Eliminate spherical aberration because their curvature is sharper than a spherical mirror, therefore rays parallel to the principle axis are never far enough away from the axis to be reflected back to a different point All parallel rays from a parabolic mirror converge at the focal point

Parabolic Mirrors - Uses Radio telescopes – receive radio signals (invisible electromagnetic waves) from outer space by using a parabolic metal surface 2. Refracting telescope – a light telescope that uses a combination of lenses to form an image (CH 15) 3. Reflecting telescope – a light telescope that uses a parabolic mirror (objective mirror) and small lenses to form an image

14.4 Color and Polarization Objectives Recognize how additive colors affect the color of light 2. Recognize how pigments affect the color of reflected light 3. Explain how linearly polarized light is formed and detected

Colors The color of an object depends on the wavelength of color that reflects from the object. All other wavelengths are absorbed by the object.

Additive Primary Colors Red, green and blue are the additive primary colors Just like white light can be dispersed into its primary colors, the primary colors can be combined to form white light Can be combined in varying proportions to form all the colors of the spectrum

Additive Primary Colors, cont. Complementary colors are formed by adding 2 of the 3 primary colors. This complementary color can then be combined with the 3rd primary color to form white light. The three complementary colors are cyan, magenta and yellow

Subtractive Primary Colors When mixing pigments, the resulting colors are different than what you’d get if you mixed light of the same colors. The mixed pigments subtract certain colors based on the frequencies of light that aren’t absorbed by the pigment. The 3 primary pigments (or primary subtractive colors) are cyan, magenta and yellow. Mixing the 3 primary pigments in proper proportions results in black because all of the primary colors are subtracted from white light.

Additive and Subtractive Primary Colors (mixing light) Subtractive (mixing pigments) Red Primary Complementary to cyan Green Complementary to magenta Blue Complementary to yellow Cyan (blue green) Complementary to red Magenta (red blue) Complementary to green Yellow (red green) Complementary to blue

Polarization of Light Waves Linear polarization is the result of the alignment of electromagnetic waves such that the vibrations of the E-fields are parallel to each other

Transmission Axis The direction in which the electric fields are polarized depends on the arrangement of molecules in the polarizing crystal. The line along which light is polarized is the transmission axis of the substance.

Horizontal Polarization Reflected light is completely polarized parallel to the reflecting surface. If the surface is parallel to the ground, the polarization is horizontal. This causes glare if light is reflected at a low angle from roads, bodies of water or car hoods.

Reducing Glare Light that is polarized horizontally causes glare. This can be filtered out by a polarizing substance whose transmission axis is oriented vertically (polarized sunglasses).

Polarization by Scattering Scattering is the absorption and reradiation of light by particles in the atmosphere. When an unpolarized beam strikes an air molecule, the electrons in the molecule vibrate in the same plane as the E-field of the incoming wave. The reradiated light is polarized in the direction of the electron oscillations.