no tagsLecture 024: Mirrors and Thin LensesYourName, 20 April 2011 (created 20 April 2011)Goals of this lectureintroduce the concepts of "real" and "virtual" imagesdiscuss the images that result from mirrorsdiscuss the images that result from simple lensesConcepts: Real and Virtual ImagesAs we have seen in the previous lecture, reflection and refraction alter thepropagation of light following well-defined laws. Technology such asmicroscopes, telescopes, cameras, contact lenses, and your own eyes relieson these two effects to form images that provide a visual representation ofreality.We will now study a subject called "geometrical optics" - the investigation ofimage formation when the wavelength of the light used to form an image isMUCH SMALLER than the object being imaged. In the last formal lecture ofthe course, we'll discuss what happens when that is no longer the case.There are two kinds of images:real images: these are formed when light comes directly from theimage to our eyes.virtual images: these are formed when light only appears to come fromthe location of the image.Demonstrate real and virtual images using a plane mirror imageand theimage of a quarter from a parabolic reflector.General Physics - E&M (PHY 1308) LectureNotesGeneral Physics - E&M (PHY 1308) LectureNotesGeneral Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Dropbox/Documents/Notebook...1 of 7 04/21/2011 08:37 AMImages with MirrorsPlane MirrorsA plane mirror is a flat, highly (perfectly) reflective surface that, when lightrays reach the surface, object the law of reflection we discussed last time:where the subscript denotes the medium in which light is propagatingbefore and after the reflection (e.g. air, water, etc.). Consider the image of aclock from the back of the classroom in a plane mirror.Let's imagine that we have a vertical arrow standing in front of the mirror,and we wish to use "ray tracing" - following reflected rays of light - to locatepoints on the virtual image. For instance, what if we wanted to locate thetop of the arrow in the virtual image? We only need two lines to locate apoint - this is a tenet of geometry. For instance, if I want to locate a point inspace I need only the intersection of two lines to do this.We can use this geometric principle and some ray tracing to figure outwhere the top of the arrow virtual image will be located. By following tworays emitted from the real top of the arrow, we can point back into themirror along the path of the reflected rays and find the intersection of therays in the virtual image. This intersection tells us where the top of thearrow in the virtual image will be located "behind" the mirror.Plane mirrors preserve an object's length and upright orientation, but theydo so by reversing front and back (not left and right - a commonmisconception). Consider if you were to point straight at the mirror. Yourvirtual image is pointing not in the same direction, but in the oppositedirection. Plane mirrors reverse coordinate axes that are perpendicular totheir surface. If the positive z-axis for the real you points into the mirror'ssurface, then the positive z-axis of your virtual image points OUT of thesurface of the mirror in exactly the opposite direction.Curved MirrorsÒ 1= Ò01General Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Dropbox/Documents/Notebook...2 of 7 04/21/2011 08:37 AMIn contrast to plane mirrors, curved mirrors form images that may beupright or inverted, virtual or real, large or small.Parabolic mirrors make the best reflectors. Why is this? The parabola has aspecial property: a line parallel to the parabola's axis makes the same angleto the normal of the parabola surface as does a second line drawn to aspecial point known as the focus or focal point of the parabola. In fact, allreflected rays in a parabolic reflector will converge to this single point. Thatmakes a parabola excellent for concentrating diffuse parallel rays down toan intense spot, or conversely taking a diffuse light source located at thefocus and generating a parallel beam of light.Close to the apex of the parabola, it's nearly indistinguishable from asphere. Thus spherical mirrors, which are cheaper and easier tomanufacture, are often substituted for parabolic mirrors. However, theapproximation of a spherical to a parabolic surface is only anapproximation, and one has to be careful or you risk manufacturing a mirrorthat doesn't focus entirely at the expected focal point.The problem of a spherical mirror that doesn't focus at the parabolic focalpoint is called spherical aberration - when the approximation to a parabolajust isn't good enough. If such distortions become bad enough, they canendanger a scientific mission (e.g. The Hubble Space Telescope).Taking the sphere as an approximation to a parabola, we can think aboutwhat images will look like when reflecting off the surface of such a mirror:Consider a spherical mirror whose center is labeled C (this is the pointwhere all the radii meet), whose focus is labeled F (where rays thatenter parallel to the mirror axis will then be reflected.Rays that travel parallel to the mirror axis will be reflected throughthe focusRays that travel through the focus will be reflected parallel to theaxisRays that travel through the center will reflect back along theirincident trajectory (since lines that go from the center, C, to themirror surface travel on radii, which means .Rays that strike the center of the mirror are reflected symmetricallyabout the axisÒ i= 0General Physics - E&M (PHY 1308) - Lecture Notes file:///home/sekula/Dropbox/Documents/Notebook...3 of 7 04/21/2011 08:37 AMConsider the following scenarios:An object located past C and F, represented by a vertical arrow:Consider a ray that leaves the point of the arrow and travelsthrough F. It must reflect parallel to the axisConsider a ray that leaves the point of the arrow and travels parallelto the axis. It must reflect through F.Where the reflected rays cross is the location of the image. Is it realor virtual?We see that rays appear to come from the image to an observer.Thus this image is REAL. The image is INVERTED, however, andlocated between the original and the mirror. It is also REDUCEDin size compared to the original object.An object located between C and F, again represented by a verticalarrowDo ray tracing for an incident parallel and incident focal ray. Showthat the image that results is REAL, ENLARGED,
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