Geometric opticsPlanar mirrorSlide 3Spherical mirrorSlide 5Slide 6Ray diagram with concave mirrorSlide 8Slide 9Slide 10Slide 11Ray diagram with convex mirrorSlide 13exampletelescope1Geometric opticsLight reflects on interface of two media, following the law of reflection:irIncident lightNormal of the interfaceReflected lightwith respect to the normal of the interface.with respect to the normal of the interface.2Planar mirrorThe image of an object in front of a planar (flat) mirror:On the other side of the mirror. The image distance di equals the object distance do.The image has the same height as the object, right side up and virtual. Concept question: when you look into a flat mirror at your image, it seems that your left and right are reversed (you raise your right hand, your image seems to raise its left hand), but not up and down (your image is still up right). If you rotate the mirror about the plane’s normal direction, your image does not rotate at all. It seems that the plane mirror has an axial symmetry about its normal direction. Then why the mirror treat left/right differently than up/down? Class discussion.3Planar mirrorThe full length mirror question asked again: Asked: what is the minimum length of this mirror for the penguin to see her full height? Asked again: what is the minimum length of this mirror for you to the penguin of her full height in the mirror?4Spherical mirrorFocal point and focal length with respect to the sphere center and its radiusConcave mirrorConvex mirror2Rf 2Rf AV123Prove: 1 = 2 = 3, so CF = FA. When A is very close to the principle axis, CF + FA ≈ CA = R.So CF ≈ 0.5R, or FV = f = 0.5RRDiscussion: in a sunny day, you are given a concave mirror and a tape measure by your mean physics professor and asked to find out the focal length of this mirror. What do you plan to do in order to survive this test?5Spherical mirrorThe object (height to the principal axis, distance to the midpoint of the mirror) and image (height, distance) relationship:The mirror equation (for both concave and convex mirrors):fddoi111oioiddhhm Together with this: One can analytically solve many problems.6Spherical mirrorThe object (height to the principal axis, distance to the midpoint of the mirror) and image (height, distance) relationship:The sign conventions:Concave mirrorconvergesConvex mirrordivergesConverge, real, upright “+”Diverge, virtual, inverted “–”7Ray diagram with concave mirrorCFObject distance: do > 2fdodihohifFrom the ray diagram: the image is up-side-down, real and shrinked.From the mirror equation:fddio111fdfddfdoooi111fd,ffffdfdd,fd,fdfddoooioooi212or0 So:1and0 m,ddhhmoioiWe get the same conclusion: the image is up-side-down, real and smaller than the object.8Ray diagram with concave mirrorCFObject distance: do = 2fdodihohifFrom the ray diagram: the image is up-side-down, real and the same size.From the mirror equation:fddio111fdfddfdoooi11112or2222fffdd,fd,ffffffdfddoioooiSo:1and1 m,ddhhmoioiWe get the same conclusion: the image is up-side-down, real and the same size as the object.9Ray diagram with concave mirrorCFObject distance: f < do < 2fdodihohifFrom the mirror equation: what conclusion can you work out? fddio111fdfddfdoooi111fd,fdfdd,df,fdfddoooioooi21or0 So:1and0 m,ddhhmoioiWe get the same conclusion: the image is up-side-down, real and larger than the object.From the ray diagram: the image is up-side-down, real and larger10Ray diagram with concave mirrorCFObject distance: do = fdodihohifFrom the mirror equation: what conclusion can you work out? fddio1110111fdfddfdoooi,dd,doii orSo: m,ddhhmoioiandWe get the same conclusion: There is no image, or the image is infinitely far away.From the ray diagram: the image seems to be far away.11Ray diagram with concave mirrorCFObject distance do < fdodihohifFrom the mirror equation: what conclusion can you work out? fddio111fdfddfdoooi111fd,fdfdd,fdfddoooiooi 1and0So:1and0 m,ddhhmoioiWe get the same conclusion: the image is up-side-down, virtual and larger than the object.From the ray diagram: the image is upright, virtual and larger12Ray diagram with convex mirrorBefore we move to all those diagrams for convex mirror, how about this problem:Use the mirror equation to prove that in the case of a convex mirror, the image is always virtual, upright and smaller than the object. fddio111Mirror equation:So:1and0 m,ddhhmoioifdfddfdoooi111Solve for 0and00 oooidf,fdfdd , or0remember1, and0 ffdfdd,fdfddooiooisoNeed to prove that and0id1m13Ray diagram with convex mirrorCFdodihohif14exampleYou place a candle 75 cm in front of a concave spherical mirror with the candle sit upright on the principal axis. The mirror is part of a sphere with a radius of R = 50 cm. You use a small while screen to find an up-side-down image of the size of 0.5 cm. What is the size of the candle?fddio111Mirror equation: And:oioiddhhm What are given: down)side(upcm50cm252cm75 .h,Rf,dioA real, up-side-down image. fdfddfdoooi111Solve for cm537cm25752575.fdfddooi, orThe fromoioiddhhm cm1cm53775)50(..ddhmhhioiioThe result15telescopeYou have two concave spherical mirrors. The first mirror is large and has a spherical radius R = 50 cm. The second mirror is small and has a spherical radius r = 5 cm. You want to construct a telescope that has a magnification of 1000 to look at the moon. State one possible
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