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Physics 202 Spring 2010 Lecture 25 Today’s topics: reflection and mirrors refraction and lenses Two types of reflection Specular reflection: reflection off a smooth surface Diffuse reflection: reflection off a rough surface Specular Reflection" Reflection from a mirror normal" !i" !r" !i = angle of incidence" !r = angle of reflection" !i = !r" object Reflection from a mirror image Reflection from a mirror image object object The image is virtual, not real. Reflection from a mirror O" O" O = object h" 90°! h" Reflection from a mirror I = image" • reflected rays seem to come from I" • Point I is located behind the mirror" at the same distance (h) as O from the mirror" • Point O and point I are on a line" perpendicular to the plane of the " mirror" 90°! h" The image is virtual, not real! I" O = object h" I = image" • reflected rays seem to come from I" • Point I is located behind the mirror" at the same distance (h) as O from the mirror" • Point O and point I are on a line" perpendicular to the plane of the " mirror" The image is virtual, not real! I" Plane (flat) mirror ! Image produced is upright ! Image is same size as the object ! Distance between the mirror and the image is the same as between the mirror and the object ! Image is a virtual image -- light rays do not pass through the image (so that image cannot be focused on a screen placed at image location) Ray diagram for plane mirror Rays are drawn from object to mirror, along with rays that reflect off the mirror. Image is where the reflected rays intersect. Since reflected rays diverge, image is behind the mirror. Convex spherical mirror Reflection from a sphere ! Convex mirror bulges in the center towards the object and viewer C = center of sphere F = focal point (apparent origin of light rays after reflection) Image of convex spherical mirror is virtual. F! C! Convex mirrors are useful because they have a larger field of view than plane mirrors ! Uses: " Car side-view mirrors • “Objects may be closer than they appear” because convex mirrors distort the scene and throw off distance perception " Stores and libraries • large field of view allows surveillance of many aisles by one person Concave mirrors can yield both real and virtual images, depending on how far away object is Concave spherical mirror ! Concave mirror curves away from the object and viewer C = center of sphere F = focal point (apparent origin of light rays after reflection) C! F! Image of far-away object in convex spherical mirror is real (light rays actually intersect at focal point). Physics 202, Lecture 25 # Refraction and Lenses ! far away object: real image ! nearby object: virtual image http://micro.magnet.fsu.edu/primer/java/mirrors/concave.html 16 Refraction : Snell’s law Refraction : Snell’s law sin !air! n =! water! sin !water! nair! sin !air! n =! water! sin !water! nair! inverted ray:! water-air case! !air = angle of incidence! normal! !air = angle of incidence! normal! !water = angle of refraction! !water = angle of refraction! n = index of refraction! !air! n = index of refraction! !air! air! water! interface! air! water! !water! interface! !water! Light ray is closer to normal in material with higher refractive index Light ray is closer to normal in material with higher refractive index Image Formed by Refraction Refraction: non parallel surfaces Example: looking at a fish R= "# i= - o(n2/n1) M=-i/o =n2/n1<1 prism! apex! o i n1 n2 n2 ! n1 + = i o R hi i M= =! ho o normal 1! normal 2! Closer, not-inverted, reduced, virtual… o = distance from glass surface to object i = distance from surface to image 19 3D view of a prism! front view of the same prism! demo: white board ! Refraction: nonparallel edges double prism! Lens: shape for which light rays that are different distances from the axis all focus at the same point apex 1! double prism! apex 1! apex 2! region in which! the rays cross! converging lens apex 2! region in which! the rays cross! converging lens lens! converging lens converging lens converging lens converging lens Thin Lenses converging lens ! Lenses are refractive optical devices with two spherical sides. R1 R2 f2 Thin focal point! f1 parallel rays! focal length f! converging lens: 3 easy rays horizontal ray goes through focal point behind lens! ray that goes through focal point in front of lens is deflected to be horizontal behind lens! ray through center of lens is undeflected! F1,F2: Focal points f=f1=f2 Focal length f>0: converging f<0: diverging Lens maker’s equation image of an object in a converging lens 30 image of an object in a converging lens converging lens optical axis! optical axis! image! Derivation of lens equation (1) converging lens 1! 1! 1! +! =! o! i! f! o-f! ho! hi! ho = height of object! o! lens formula! f! i! f! hi = height of image! from similar triangles,! ho o " f = hi f ! Derivation of lens equation (3) Derivation of lens equation (2) o! ho o " f = hi f i! ho! ho = height of object! hi! hi = height of image! So,! ! from similar triangles,! i o h o = " o = hi ho hi i ! ! and! o o"f = i f ! o o = "1 i f 1 1 1 = " i f o 1 1 1 + = i o f o ho = i hi Lens equation!