Reflection of Light Reflection – The bouncing back of a particle or wave that strikes the boundary between two media. Law of Reflection – The angle of incidence equals the angle of reflection. Incident rays and reflected rays make equal angles with a line perpendicular to the reflecting surface, called the normal. Diffuse Reflection – The reflection of waves in many directions from a rough surface. Each ray obeys the law of reflection. Specular Reflection – The reflection of wave in one direction from a smooth surface. Plane (flat) Mirrors can only produce virtual images. Virtual Image - An image formed from light rays that only appear to be coming from behind the reflecting surface.

Reflection (cont.)

Curved Mirrors Concave Spherical Mirror – An inwardly curved mirror that is a portion of a sphere and that converges incoming light.

Concave (cont.) Concave mirrors form real images and virtual images. Real Image – An image formed when rays of light actually intersect at a single point.

Rules for Drawing Reference Rays Concave Mirrors Line drawn from object to mirror: Parallel to principal axis. Through focal point. Through center of curvature C. Line drawn from mirror to image after reflection: Through focal point F. Back along itself through C

Vocabulary for Rules Center of Curvature (C) – The distance from the mirror’s surface to the center of the sphere of which the mirror is a small part. Focal Point (F) – For a spherical mirror, the focal point is equal to half the radius of curvature. Principal Axis -  A line passing through the center of the surface of a lens or spherical mirror and through the centers of curvature of all segments of the lens or mirror. 

Convex Mirrors An outwardly curved mirrored surface that is a portion of a sphere and that diverges incoming light. Convex mirrors form virtual images only.

Rules for Drawing Reference Rays Convex Mirrors Same as for concave mirrors, except that the focal point and center of curvature are behind the mirror’s reflective surface. We draw dashed lines along the reflected reference rays to points behind the mirror. Mirror Equation: 1/f = 1/di + 1/do f = focal length di = image distance Do = object distance

Lenses Lens – A transparent object that refracts light rays, causing them to converge or diverge to form an image. Refraction – The bending of a wave as it passes at an angle from one medium to another. If the wave slows down it will be bent toward the normal. If the wave speeds up it will be bent away from The angle is measured from

Index of Refraction Index of Refraction – The ratio of the speed of light (c) in a vacuum to the speed of light (v) in a given material. Index of Refraction Equation: 𝑛= 𝑐 𝑣 n = index of refraction c = speed of light in a vacuum v = speed of light in a given material. The index of refraction is never less than 1. The index of refraction for air is 1.00. There are no units for the index of refraction.

Example Calculate the speed of light in a diamond. n=c/v List the givens: n = 2.42 (from table) c = 3.0 x 108 m/s v = ? v = c/n = 3.0 x 108 m/s / 2.42 = 1.24 x 108 m/s

Snell’s Law Snell’s Law - A relationship between the path taken by a ray of light in crossing the boundary or surface of separation between two contacting substances and the refractive index of each. Snell’s Law Equation: n1 sin θ1 = n2 sin θ2 n = index of refraction for each material θ = angle of refraction for each material

Example Light strikes a flat piece of glass at an incident angle of 60°. If the index of refraction of the glass is 1.50, what is the angle of refraction in the glass?

Converging Lens (Convex) Converging Lens - A lens that is thickest in the middle causing parallel rays of light to come to a focus. Forms real or virtual images.

Converging Lens (Cont) If an object is located outside the focal point of a converging lens, the image it forms is real, inverted, and on the opposite side of the lens. If an object is located inside the focal point of a converging lens, the image it forms is virtual, upright, enlarged, and on the same side as the object. If the object is at the focal point, the rays do not converge and therefore no image is formed.

Rules for Drawing Ray Diagrams for Converging Lenses Draw a ray from the object parallel to the principal axis to the center of the converging lens, then through the focal point on the opposite side of the lens. Draw a ray through the focal point on the same side of the lens as the object to the center of the lens, then parallel to the principal axis. Draw a ray that passes through the center of the lens and continue in the same direction that it had when it entered the lens.

Diverging Lens (Concave) Diverging Lens - A lens that causes a beam of parallel rays to diverge after refraction, as from a virtual image; a lens that has a negative focal length.

Diverging Lens (Concave) The focal length of a diverging lens is always a negative number. The image formed by a diverging lens is always virtual, upright, smaller, and on the same side of the lens as the object.

Rules for Drawing Ray Diagrams for Diverging Lenses Draw a ray parallel to the principal axis to the center of the lens and travel in line with the focal point on the same side as the object. (i.e., in a direction such that its extension will pass through the focal point). Draw a ray towards the focal point on the opposite side of the lens as the object to the center of the lens, then parallel to the principal axis. Draw a ray that passes through the center of the lens and continue in the same direction that it had when it entered the lens.

Mirror/Lens Equation 1 1 1 ----- = ----- + ----- f p q or ----- = ----- + ----- f do di

Sign Convention for Lenses + - Object in front of lens in back of lens Image in back of lens in front of lens Focal converging lens diverging lens length

Magnification Equation hi di M = ---- = - ---- ho do ho=object height, hi = image height, M = magnification, or do=object distance, di = image distance, M = magnification Sign of M Upright + Inverted - *Same equations are used for lenses.

Color and Polarization Additive Primary Colors = Red, Green, and Blue. When you combine the three additive primary colors, you produce white light. Subtractive Primary Colors = Cyan, Magenta, and Yellow. When you combine the three subtractive primary colors, you filter out all light.

Primary Additive and Subtractive Colors Red Magenta Yellow Green Cyan Blue

Polarization Polarization – The alignment of electromagnetic waves in such a way that the vibrations of the electric fields in each of the waves are parallel to each other.

Homework Pg 536 1 and 2 Pg 540 1 and 2 add ray diagrams to both.

Convex (cont.) Summary of Curved Mirrors: