Lecture 36 Chapter 35 36 Images Interference Mirrors Review Plane flat mirror Concave caved in away from object Convex flexed out toward object Real images on side where object is virtual images on opposite side Plane and convex mirrors make only virtual images Concave mirrors can produce both real and virtual images Review Spherical mirrors have focal point r is radius of curvature f 12 r Find focal length f from 1 1 1 p i f Object distance p is Image distance i is for real images for virtual images f is for concave for convex Review Ratio of image s height h to object s height h is called lateral magnification m h m h Magnification also equal to i m p m is if image has same orientation as object m is if image is inverted from object Plane mirror m 1 Review Mirrors Mirror Type Object Location Image Location Image Size Image Type Image Orientation Sign of f Sign of i Sign of m Plane Anywhere i p Equal Virtual Same 1 Concave p f Anywhere Bigger Virtual Same Concave f p 2f i 2f Bigger Real Invert Concave p 2f i 2f Equal Real Invert Concave p 2f 2f i f Smaller Real Invert Convex Anywhere i f Smaller Virtual Same Review Thin Lenses Light rays bent by refraction form an image Converging lens with convex refracting sides Diverging lens with concave sides Thin Lenses Review Real images form on opposite side of lens from object virtual images on same side Diverging lens only produces smaller same orientation virtual images like convex mirror Converging lens like concave mirror can produce both real and virtual images depending on where the object is in relation to the lens focal point Review Thin lenses have a focal point on each side of lens Focal length f same as mirror 1 1 1 p i f Lens maker s equation for lens in air r1 is radius of lens surface nearest the object r2 is other surface r is for convex surface for concave surface 1 1 1 n 1 f r1 r2 Thin lenses Review Lateral magnification m same as for mirror i m p For a system of lenses or mirrors the total magnification M is product of each m M m1m2 m3 Work through system of lenses one by one use image from one lens as object for next lens Review Thin Lenses Converging lens concave mirror Diverging lens convex mirror Thin Lens Type Object Location Image Location Image Size Image Type Image Orientation Sign of f Sign of i Sign of m Converging p f Anywhere Bigger Virtual Same Converging f p 2f i 2f Bigger Real Invert Converging p 2f i 2f Equal Real Invert Converging p 2f 2f i f Smaller Real Invert Diverging Anywhere i f Smaller Virtual Same Lecture 36 cont Chapter 36 Interference Interference 1 Light is an EM wave Interfering light waves combine to enhance or suppress colors in sunlight Soap bubbles oil slicks Interference best evidence that light is a wave Huygen s principle points on wavefront act as point sources of spherical wavelets at time t new position of wavefront is tangent to wavelets Interference 2 Can use Huygen s principle and geometry to prove Snell s law see section 36 2 n2 sin 2 n1 sin 1 Wavelength of light in two different media 1 and 2 are proportional to 1 v1 sin 1 n2 2 v2 sin 2 n1 Interference 3 1 v1 sin 1 n2 2 v2 sin 2 n1 Frequency of light in medium is same as in vacuum Wavelength and velocity of light change in a medium and depend on its index of refraction n Velocity of light in a medium is always smaller than speed of light in vacuum c Wavelength of light in a medium n is smaller than in vacuum and related by n n Interference 4 Phase difference between 2 light waves can change if waves travel through different media with different n Number of wavelengths in media N1 L n1 Ln1 N2 n 2 Phase difference in terms of N 2 N1 Ln2 Ln1 L L Ln2 n2 n1 Interference 5 Checkpoint 2 Rays have same wavelength and initially in phase A If 7 6 wavelengths fit within top material and 5 5 fit within bottom which has greater index of refraction n Larger n produce smaller n Which material has smallern Smaller more wavelengths in same distance Top material has greater index of refraction n Interference 6 Checkpoint 2 Rays have same wavelength and initially in phase B After material will interference of waves give brightest bright intermediate dark intermediate illumination or darkness Look at phase difference in terms of L N 2 N 1 n 2 n1 Given of wavelengths for each material N 2 N1 7 6 5 5 2 1 Waves are 2 1 wavelengths out of phase after passing through materials Interference 7 Checkpoint 2 B After material will interference of waves give brightest bright intermediate dark intermediate illumination or darkness If phase difference is an integer of wavelengths 0 1 2 then waves are in phase and have full constructive interference brightest spot Effective phase difference is decimal fraction Total phase difference 2 1 Effective phase difference 0 1 Interference 8 Checkpoint 2 B After material will interference of waves give brightest bright intermediate dark intermediate illumination or darkness If phase difference is 0 5 wavelengths half a wavelength then waves are completely out of phase and fully destructive interference dark spot Our effective phase difference of 0 1 is closer to 0 than 0 5 so intermediate bright spot but not the brightest Interference 9 For interference pattern to appear waves must have a constant phase difference If phase difference does not vary with time waves are coherent Light is produced by emission from individual atoms Atoms in conventional light light bulbs sunlight are in random phases so light is incoherent Lasers are designed so atoms emit coherent and monochromatic light
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