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March 29, 2005 Physics for Scientists&Engineers 2 1Physics for Scientists &Physics for Scientists &EngineersEngineers 22Spring Semester 2005Lecture 38March 29, 2005 Physics for Scientists&Engineers 2 2ReviewReview! The index of refraction of an optical material, n, is given by•c is the speed of light in a vacuum•v is the speed of light in the optical material•n ! 1, nvacuum =1• We will use nair = 1! The Law of Refraction or Snell’s Lawcan be expressed asn =cvn1sin!1= n2sin!2March 29, 2005 Physics for Scientists&Engineers 2 3LensesLenses! When light is refracted crossing a curved boundary between twodifferent media, the light rays follow the law of refraction ateach point on the boundary! The angle at which the light rays cross the boundary is differentalong the boundary, so the refracted angle is different atdifferent points along the boundary! A curved boundary between two optically transparent media iscalled a lens! Light rays that are initially parallel before they strike theboundary are refracted in different directions depending on thepart of the lens they strike! Depending of the shape of the lens, the light rays can be focusedor caused to divergeMarch 29, 2005 Physics for Scientists&Engineers 2 4Lens Maker FormulaLens Maker Formula! If the front surface of the lens is part of the surface of a sphere withradius R1 and the back surface of the lens is part of the surface of asphere with radius R2, then we can calculate the focal length f of thelens using the lens-makers formula! Note that in this equation R2 is negative because it has the oppositecurvature from the front surface! If we have a lens with the same radii on the front and back of the lensso that R1 = R2 = R, we get1f= n !1( )1R1!1R2"#$%&'1f=2(n ! 1)RMarch 29, 2005 Physics for Scientists&Engineers 2 5Lens Focal LengthsLens Focal Lengths! Unlike mirrors, lenses have a focal length on both sides! Light can pass through lenses whilemirrors reflect the light allowingno light on the opposite side! The focal length of aconvex (converging) lens is definedto be positive! The focal length of aconcave (diverging) lens isdefined to be negative.Convex (converging) lensConcave (diverging) lensMarch 29, 2005 Physics for Scientists&Engineers 2 6Convex LensesConvex Lenses! A convex lens is shaped such that parallel rays will be focused byrefraction at the focal distance f from the center of the lens! In the drawing on the right, a light ray is incidenton a convex glass lens! At the surface of the lens, the light ray isrefracted toward the normal! When the ray leaves the lens, it isrefracted away from the normal! Let us now study the case of severalhorizontal light rays incident on aconvex lens! These rays will be focused to a point adistance f from the center of the lens onthe opposite side from the incident raysMarch 29, 2005 Physics for Scientists&Engineers 2 7Thin LensesThin Lenses! The rays enter the lens, get refracted at the surface, traverse thelens in a straight line, and get refracted when they exit the lens! In the third frame, we represent the thin lens approximation bydrawing a black dotted line at the center of the lens! Instead of following the detailed trajectory of the light rays inside thelens, we draw the incident rays to the centerline and then on to thefocal point! This real-life lens is a thick lensand there is displacementbetween the refraction at theentrance and exit surfaces! We will treat all lenses as thinlenses and treat the lens as a lineat which refraction takes placeMarch 29, 2005 Physics for Scientists&Engineers 2 8Images with Convex LensesImages with Convex Lenses! Convex lenses can be used to form images! We show the geometric construction of the formation of an image usinga convex lens with focal length f! We place an object standing on the optical axis represented by thegreen arrow! This object has a height ho and is located a distance do from the centerof the lens such that do > fMarch 29, 2005 Physics for Scientists&Engineers 2 9Images with Convex Lenses (2)Images with Convex Lenses (2)! We start with a ray along the optical axis of the lens that passesstraight through the lens that defines the bottom of the image.! A second ray is then drawn from the top of the object parallel tothe optical axis• This ray is focused through the focal point on the other side of the lens! A third ray is drawn through the center of the lens that is notrefracted in the thin lens approximation! A fourth ray is drawn fromthe top of the objectthrough the focal point onthe same side of the lensthat is then directedparallel to the optical axisMarch 29, 2005 Physics for Scientists&Engineers 2 10Images with Convex Lenses (3)Images with Convex Lenses (3)! Now let us consider the image formed by an object with height placeda distance from the center of the lens such that do < f! The first ray again is drawn from the bottom of the object along theoptical axis! The second ray is drawn from the top of the object parallel to theoptical axis and is focused through the focal point on the opposite side! A third ray is drawn through thecenter of the lens! A fourth line is drawn such thatit originated from the focal pointon the same side of the lens andis then focused parallel to theoptical axis• These three rays are diverging! A virtual image is located on thesame side of the lens as the objectMarch 29, 2005 Physics for Scientists&Engineers 2 11Concave LensesConcave Lenses! A concave lens is shaped such that parallel rays will be caused todiverge by refraction such that their extrapolation would intersect at afocal distance from the center of the lens on the same side of the lensas the rays are incident! Assume that a light ray parallel tothe optical axis is incident on aconcave glass lens! At the surface of the lens, thelight rays are refracted towardthe normal! When the rays leave the lens, they are refracted away from the normalas shown! The extrapolated line shown as a red and black dashed line that pointsto the focal point on the same side of the lens as the incident rayMarch 29, 2005 Physics for Scientists&Engineers 2 12Concave Lenses (2)Concave Lenses (2)! Let us now study several horizontal light rays incident on a concave lens! After passing through the lens, the rays will diverge such that theirextrapolations intersect at a point a distance f from the center of the lens onthe same side of the lens as the incident rays! To the right is a concave lens with fiveparallel lines of light incident in the


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MSU PHY 184 - PHY184-Lecture38n

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