Specular Reflection" !i =!r" Physics 202 Spring 2010 Lecture 25. Two types of reflection. Reflection from a mirror
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1 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
2 Reflection from a mirror Reflection from a mirror image image object object The image is virtual, not real. Reflection from a mirror Reflection from a mirror O" O" h" h" 90! O = object 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! h" h" 90! O = object 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" I"
3 Plane (flat) mirror Ray diagram for plane 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) 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) F! C! Image of convex spherical mirror is virtual.
4 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 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). Concave mirrors can yield both real and virtual images, depending on how far away object is! far away object: real image # Refraction and Lenses Physics 202, Lecture 25! nearby object: virtual image 16
5 Refraction : Snell s law Refraction : Snell s law sin! air! sin! water! =! n water! n air! inverted ray:! water-air case! sin! air! sin! water! =! n water! n air!! air! normal! air!! air = angle of incidence!! water = angle of refraction! n = index of refraction! interface! water!! water! Light ray is closer to normal in material with higher refractive index! air! normal!! water! air! water!! air = angle of incidence!! water = angle of refraction! n = index of refraction! interface! 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(n 2 /n 1 ) M=-i/o =n 2 /n 1 <1 prism! apex! o i normal 1! normal 2! n 1 i + n 2 o = n 2! n 1 R M = h i h o =! i o 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!
6 double prism! Refraction: nonparallel edges apex 1! Lens: shape for which light rays that are different distances from the axis all focus at the same point double prism! apex 1! lens! apex 2! region in which! the rays cross! apex 2! region in which! the rays cross!
7
8 Thin Lenses! Lenses are refractive optical devices with two spherical sides. R 1 R 2 f 2 Thin focal point! f 1 F 1,F 2 : Focal points f=f 1 =f 2 Focal length parallel rays! focal length f! Lens maker s equation f>0: converging f<0: diverging 30 : 3 easy rays image of an object in a converging lens horizontal ray goes through focal point behind lens! ray through center of lens is undeflected! ray that goes through focal point in front of lens is deflected to be horizontal behind lens!
9 image of an object in a converging lens optical axis! optical axis! image! Derivation of lens equation (1) o! f! i! 1! 1! o! +! 1! i! =! f! lens formula! o-f! h o! h o = height of object! from similar triangles,! f! h i! h i = height of image! h o h i = o " f f
10 Derivation of lens equation (2) Derivation of lens equation (3) h o! o! i! h o h i = o " f f and! o i = h o h i h o = height of object! from similar triangles,! i h i = o h o " h o h i = o i h i! h i = height of image! So,! o = o " f i f o = o i f "1 1 i = 1 f " 1 o 1 i + 1 o = 1 f Lens equation!
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