Reflection and Refraction Optics Reflection and Refraction

Reflection When a wave encounters a new medium or barrier some of the wave is bounced back (reflected), and some is transmitted (refracted)

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

Image Types Real – Light rays actually travel to that location Virtual – Light appears to be at that location Upright – image is right side up compared to object Inverted – image is upside down as compared to object

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

Plane (flat) Mirror Mirror

Huygens Principle Every point on a propagating wave front serves as a source of a spherical secondary wavelet The corresponding spherical wavelets produce further wave fronts Basis for Diffraction, Reflection, Refraction

Huygens Principle

Huygens Principle

Huygens Principle First proposed explanation that light is a wave Newton later proposed that light is a particle

Question Compared to running down the road, if you were to run in thick mud…. Would you go as fast? Speed decreases Would your steps be as long? Wavelength decrease

Refraction Changing of speed when wave enters new material (frequency remains constant) Speed decreases in more dense material Wavelength decreases Speed increases in less dense material Wavelength increases

Refraction Example Freqair=Freqwater because the color remains the same Since the wavelength changes, the velocity must change proportionately Air Water

Index of Refraction (n) Measure of the optical density of a material Table in the Reference Tables

Refraction When a wave enters a new medium, it changes speed. When a wave enters a new medium, it changes direction Simulation

Refraction

Refraction

Snell’s Law n1 sin θ1 = n2 sin θ2 Air Water θi θr

Snell’s Law When a wave enters a more dense material, the wave will bend TOWARDS the normal When a wave enters a less dense material, the wave will bend AWAY from the normal

Example n1 sin θ1 = n2 sin θ2 θr= 58.7° Air Water n = 1.00 n = 1.33 40°

Example θi= 47° θr= 76.6° θi= 48° θr= 81.3° Air Water n = 1.00 n = 1.33 θi= 47° θr= 76.6° θi= 48° θr= 81.3° θi= 49° θr= ? Is there a problem? θr=?

Total Internal Reflection At a certain incident angle the refracted ray will be at 90°. Critical Angle,θc At angles greater than the Critical Angle, the ray is reflected back into the material. θi Air Water n = 1.00 n = 1.33 θr

Total Internal Reflection n1 sin θC = n2 sin θ2 sin θ2 = 1 n1 sin θC = n2 n1 > n2

Dispersion Spreading of light into its color components Index of refraction is based on frequency of light Index varies for different frequencies

Dispersion

Curved Mirrors and Lenses

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