Optics Mirrors and Lenses

Law of Reflection Angle of Incidence = Angle of Reflection θi = θr Always measured from Normal(Perpendicular) θi θr

Plane Mirror Flat, smooth surface from which light is reflected. The distance the object is away from the mirror is equal to the distance the image appears to be “in” the mirror

Vocabulary Object distance, do Image distance, di Distance object is from optical device Image distance, di Distance image is from optical device

Vocabulary Object Height, ho Image Height, hi Height of object Height of image

Vocabulary Real Image Image formed by actual intersection of light rays Image can be projected on a screen di=(+)

Vocabulary Virtual Image (imaginary) Light rays do not intersect Image can NOT be projected on screen The eye traces back the rays to where they appeared to have once intersected di=(-)

Vocabulary Upright Image Inverted Image Object Image Upright Image Image is of the same orientation as object hi = (+) Inverted Image Image is inverted from the orientation of the object hi = (-) Object Image

Vocabulary Magnification, M Ratio of the image height to the object height M=(+) image is upright M=(-) image is inverted

Plane Mirror Mirror do = -di ho=hi M=1

Spherical Mirrors Concave Mirrors Convex Mirrors Mirror surface is on the inside of the curve Convex Mirrors Mirror surface is on the outside of the curve

Focal Point Point where light converges Half the radius f C

Concave Mirror Ray that is initially parallel to central axis reflects through focal point Ray that is initially through focal point reflects parallel to central axis Ray that is incident at vertex, reflects at same angle Ray that travels through center of curvature will reflect back through center of curvature

Concave Mirror f C

Mirror Equation

Example f C do = 30 cm f = 10 cm di = ? di = 15 cm M = -0.5

Convex Mirror Ray that is initially parallel to central axis reflects through virtual focal point Ray that is initially through virtual focal point reflects parallel to central axis Ray that is incident at vertex, reflects at same angle Ray that travels through center of curvature will reflect back through center of curvature

Example f C

Example di = ? f = -10 cm do =15 cm di = -6 cm M = 0.4

Lenses Converging Lenses Diverging Lenses Biconvex f=(+) Biconcave

Converging Lens Rays Ray that is initially parallel to central axis will refract through far focal point Ray that is initially through near focal point will refract parallel to central axis Ray that passes through center of lens pass without refraction

Converging Lens

Converging Lens Example f = 10 cm di= ? do = 20 cm di= 20 cm M = 1

Diverging Lens Rays Ray that is initially parallel will refract as if coming from near focal point Ray that is initially through far focal point will refract as if coming from parallel Ray that passes through center will continue on

Diverging Lens

Diverging Lens Example do = 25 cm f = -10 cm di = ? di = -7.14 cm M = 0.3

Lenses in Combination Image from the first lens becomes the object for the second lens

Lenses in Combination

Lenses in Combination do1 = 25 cm f2 = 8 cm di2 = 12 cm f1 = 10 cm