Lecture 37:Lecture 37: MON 20 APRMON 20 APRPhysics 2102Jonathan DowlingOptics: ImagesOptics: ImagesThin LensesThin Lensesfip111=+For small angles and thin lenses, Convergent: f positiveDivergent: f negative!"#$%&''=2111)1(1rrnfLens maker’s equationConvergent lensDivergent lensImages due to lenses:• An object placed beyond a convergent lenses’ focal point, will produce a real, inverted image on the other side of the lens. This is the principle used in projectors.• An object placed between a convergent lens and its focal point will produce a virtual image on the same side as the object.•Divergent lenses always produce a virtual image on the same side asthe object.• Real images have i positive in formulas, virtual images have i negative.Locating images by drawing rays:• A ray of direction initially parallel to the axis will pass through the focal point.• A ray that initially has a direction thatpasses through the focal point will emerge parallel to the central axis.• A ray going through the center of thelens will be undeflected. • The image of a point appears where all rays emanating from a point intersect.ExampleExample• An object 1.2cm high is placed 4cm from a bi-convex lens withr1=10cm and r2=15cm. Find the position and size of the image.• A second lens of focal length +6cm is placed 12cm to the right ofthe first lens. Find the position and size of the new image.Images fromImages fromspherical mirrorsspherical mirrorsfip111=+Consider an object placed between the focalpoint and the mirror. It will produce a virtualimage behind the mirror.When the object is at the focal point theimage is produced at infinity.If the object is beyond the focal point, a realimage forms at a distance i from the mirror.Check the signs!!pim !=lateralmagnificationThin LensesThin Lensesfip111=+For small angles and thin lenses, Convergent: f positiveDivergent: f negative!"#$%&''=2111)1(1rrnfLens maker’s equationConvergent lensDivergent lensLocating images by drawing rays:• A ray of direction initially parallel to the axis will pass through the focal point.• A ray that initially has a direction thatpasses through the focal point will emerge parallel to the central axis.• A ray going through the center of thelens will be undeflected. • The image of a point appears where all rays emanating from a point intersect.Images due to lenses:• An object placed beyond a convergent lenses’ focal point, will producea real, inverted image on the other side of the lens. This is the principleused in slide projectors.• An object placed between a convergent lens and its focal point willproduce a virtual image on the same side as the object.•Divergent lenses always produce a virtual image on the same side asthe object.• Real images have i positive in formulas, virtual images have i negative.ExampleExample• An object 2cm high is placed 4cm from a bi-convex lens withr1=10cm and r2=15cm, and index of refraction n=1.5. Find theposition and size of the image.• A second lens of focal length +6cm is placed 12cm to the right ofthe first lens. Find the position and size of the new
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