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The Geometric Optics of Image Formation Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science (I) Clear Materials Bend Rays Light bending is called "refraction". ray Air Water where the ray really comes from. Imaging Science Fundamentals where a straight ray would come from. Chester F. Carlson Center for Imaging Science Refraction The amount of bending depends on a property of the material called "index of refraction", n. Water n is low Imaging Science Fundamentals Glass n is high Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Refraction “wavefronts” Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Refraction “wavefronts” separated by one wavelength Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Index of refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Velocity in other media is less than c: Medium vacuum air water glass diamond Imaging Science Fundamentals velocity 3 x 108 m/s 2.999 x 108 m/s 2.26 x 108 m/s 2 x 108 m/s 1.25 x 108 m/s Chester F. Carlson Center for Imaging Science Index of refraction The index of refraction, n, of a medium is defined as the ratio of the speed of light in a vacuum to the speed in that medium: n = c/v Medium vacuum air water glass diamond Imaging Science Fundamentals velocity 3 x 108 m/s 2.999 x 108 m/s 2.26 x 108 m/s 2 x 108 m/s 1.25 x 108 m/s n 1 1.0003 1.33 1.5 2.4 Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Glass: V = 200,000,000 m/s Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Glass: V = 200,000,000 m/s Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Glass: V = 200,000,000 m/s Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Glass: V = 200,000,000 m/s Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Glass: V = 200,000,000 m/s Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Glass: V = 200,000,000 m/s Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Glass: V = 200,000,000 m/s Chester F. Carlson Center for Imaging Science Refraction The velocity of light in a vacuum is a fundamental constant: c = 3 x 108 m/s Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Glass: V = 200,000,000 m/s Chester F. Carlson Center for Imaging Science Vacuum V = 300,000,000 m/s Imaging Science Fundamentals Glass: V = 200,000,000 m/s Chester F. Carlson Center for Imaging Science Refraction for Different Materials light 45 AIR WATER GLASS 16 Imaging Science Fundamentals 28 32 DIAMOND Chester F. Carlson Center for Imaging Science Snell’s Law: n1sin1= n2sin2 Examples 1 Material #1 n1 n2 2 Material #2 Material Vacuum Air Water Glass Diamond Imaging Science Fundamentals Index of Refraction, n 1 (exactly) 1.0003 (approximately 1.000) 1.33 1.5 2.4 Chester F. Carlson Center for Imaging Science Snell’s Law: The equations 1 Material #1 n1 n2 2 Material #2 Snell’s Law: n1sin1= n2sin2 Define n = 1 for a vacuum All other values of n are >1. Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Snell’s Law: n1sin1= n2sin2 It works exactly the same in reverse. 1 Material #1 n1 n2 2 Material #2 Material Vacuum Air Water Glass Diamond Imaging Science Fundamentals Index of Refraction, n 1 (exactly) 1.0003 (approximately 1.000) 1.33 1.5 2.4 Chester F. Carlson Center for Imaging Science Into and out of a flat plate of glass. Glass n2 = 1.5 Air, n1 = 1.00 Air, n3 = 1.00 4 n1sin1= n2sin2 1 Imaging Science Fundamentals 3 2 n3sin3= n4sin4 Chester F. Carlson Center for Imaging Science 2= 3 1= 4 It can be shown that and the input and output rays are parallel. Glass n2 = 1.5 Air, n1 = 1.00 Air, n3 = 1.00 4 3 1 Imaging Science Fundamentals 2 Chester F. Carlson Center for Imaging Science Using Refraction to Focus Light. n1=1 Parallel Rays Glass Lens in Air n1=1 n2=1.5 Focal point of lens Optical Axis Focal length of lens, f Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Parallel rays come to focus at one point on the image plane. n1=1 Glass Lens in Air n1=1 n2=1.5 Optical Axis Image Plane Focal length of lens, f Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science A Chief Ray is a ray heading toward or away from the center of the lens. n1=1 Glass Lens in Air n1=1 Examples of Chief Rays n2=1.5 Optical Axis Focal length of lens, f Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science Thin Lens Approximation: Chief Rays pass through the lens without deviation. n1=1 Glass Lens in Air n1=1 Examples of Chief Rays n2=1.5 Optical Axis Focal length of lens, f Imaging Science Fundamentals Chester F. Carlson Center for Imaging Science
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