Unit I : Pinholes, Parallax, and Reflection Light rays, boundary rays: drawn to see where to stand to see an image Pinhole cameras: image is upsidedown relative to the object use similar triangles, magnification equation one light ray from point makes it to the screen moving object closer to pinhole image will increase in size moving screen farther from pinhole image will increase in size larger pinhole loses focus Solving Pinhole Cameras screen h 5' h = h' image is flipped S n' S s' but h' is still (+) pinnole Parallax: nearer objects shift more Lvs R observers have different views Left eye: sees more right Switch to right eye: region you see is more left than before object moves opposite of eye open Angular size: smaller object appears to be the same size as a larger object far away. use similar triangles (apparent size) Linear Size: actual size calculating angular size: Looking through a hole: L I L I of D d 0 I = d I = d L D L D+d
Shadows boundary ray reaches from one light source: partial shadow boundary rays reach from both light sources: full shadow boundary rays don't reach from either: full light extended light source: fuzzy edges point light source: solid edges Mirrors Plane mirrors: image is straight across from object, infinite focal length standing to see image in mirror: Draw image directly across from object Oraw boundary rays Image in boundary ray: can view How much you can view in a mirror: similar triangles Ia D d = I eye L 0= dL b L ( Looking glass view: image 500 cm 30 cm x object = mirror 50 cm 400cm 500cm 240cm 80cm X Q 12,000 cm = 50 cmx 300 cm 50cm 50cm 300 cm x = 240 cm of tree 400cm Mirror angle problems extend mirrors normal perpendicular to the mirror incident and reflected: same angle in respect to the normal parallel lines: create the same angle
Law of Reflection reflected ray on the other side of the normal is the same angle as the incident ray incident normal reflected B. e r O, = Gr mirror Virtual Image: tracked back light rays from point on an object that reflects off of a mirror. Looking at a mirror, you see your own virtual image Multiple Plane Mirrors: image created by one mirror becomes the object for second mirror Dead zone: image behind all mirrors. End point. Concave mirror: edges closer to you, cave. Convex mirror: middle closer to you. Focal point: half way between mirror and center if mirror continued and made a sphere, zf= Mirror equation: S= object distance (always positive) I 1 I + = S S' f 5' = image distance f= focal length . Magnification equation: m = h' = -s' h'= image height h S h= object height . Li ight rays from object always go through image itself
concave Mirror (object outside f) image: real, inverted, in front of mirror, larger or smaller optical axis s' = positive h' = negative f= positive Concave Mirror (object inside f) image: virtual, upright, behind mirror, larger, farther -optical axis s' = negative h'= positive f= positive Convex Mirror image: virtual, upright, behind mirror, smaller, closer - optical axis s'= negative f 'h' = positive F= negative Plane Mirror image: virtual, upright, same size and distance - optical axis as the object 1 f = o
Unit 2: Bending Light: Cameras and Vision Snell's Law: n,sing,=nissing, Smaller n, closer to the Surface Larger n, closer to the normal Fish in a tank: can see more because light bends towards the surface once out of the water into the air. Air has a smaller n than water. Total Internal Reflection: no refracted ray largest ratio of n's n2 must be less than n, because sin-1 has a max Ocr = sin-' infinali "start, output of I if Or is 90. rewrite Snell's Law as Dispersion: material of different h's for different wavelengths of light so each ray refracts at a different angle greater change in n refracts more Person looking in a pool of water, what is the farthest they can see in the bottom of the pool? hwater =1.33 n, sing;=nzsiner 480 nair =1 Isin(45")1.335in Or S or .71=1.33 sin 9 , Im .53=sinor sin-1 (.53)=32° Or=32° I m tan == opposite adjacent tan(320) = opposite +an (320)(1)=.62 can see .62m of the bottom of the pool.
Converging Lens (object outside f) image: real, inverted, behind the lens 5' = positive optical axis - h'=negative f= positive Converging Lens (object inside f) image: virtual, upright, in front of lens, larger s' =negative n' = positive optical axis - f = positive Diverging Lens image: virtual, upright, in Front of lens, smaller S' = negative h'= positive f= negative
Lens Equations and Compound Optics - more distant object image closer to focal point - shift focus closer to object more film further from lens - further object= closer image decrease distance between lens and film, but relax eye to increase focal length - closer object= farther image increase distance between lens and film, but contract eye to decrease the focal length - compound optics : image of one lens) mirror becomes another, multiple lenses I mirrors - CIS: closer image=farther object inc lens+film, contract eye shorten f - opposite for farther object Corrective Lenses myopia near-sighted diverging (on My the test is Near, I might Die) diverging lens increases focal point of the eye, decreases power looks smaller hyperopia far-sighted converging converging lens decreases the focal point of the eye, increases power looks closer Lens Power p= P=P, + P2 power is measured in diopeters (meters)