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WAVES

WAVES. MEDIUM VIBRATES PERPENDICULARLY TO THE WAVE DIRECTION IF f IS THE WAVE FREQUENCE AND λ IS THE WAVELEGTH THEN c, THE WAVE VELOCITY, IS GIVEN BY: c = λ f EXAMPLES ELECTROMAGNETIC WAVES WAVES IN A STRING. ELECTROMAGNETIC WAVES.

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WAVES

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  1. WAVES • MEDIUM VIBRATES PERPENDICULARLY TO THE WAVE DIRECTION • IF f IS THE WAVE FREQUENCE AND λ IS THE WAVELEGTH THEN c, THE WAVE VELOCITY, IS GIVEN BY: c = λf • EXAMPLES • ELECTROMAGNETIC WAVES • WAVES IN A STRING

  2. ELECTROMAGNETIC WAVES • FOR EVERY ELECTRIC WAVE THERE IS A CORRESPONDING MAGNETIC WAVE AT RIGHT ANGLES TO IT (AND VICE VERSA).

  3. LONGITUDINAL WAVES • PARTICLE MOTION IS PARALLEL TO THE WAVE DIRECTION • EXAMPLE – SOUND WAVES

  4. ELECTROMAGNETIC (E-M) SPECTRUM • E-M WAVES IN NATURE RANGE FROM λ=.01 nm TO λ=1,000 m, A RANGE OF 1013. • 1 ANGSTROM = 10-8 CM • FROM SHORT TO LONG WAVELENGTH: • GAMMA (γ) RAYS • X-RAYS • ULTRA-VIOLET (UV) RAYS • VISIBLE RAYS (LIGHT) • INFRA-RED (IR) RAYS • RADIO WAVES • TWO ATMOSPHERIC WINDOWS (LIGHT AND RADIO)

  5. REFLECTION • REACTION OF LIGHT WAVES WHEN THEY ENCOUNTER AN OPAQUE MEDIUM i=r WHERE: iIS THE ANGLE OF INCIDENCE rIS THE ANGLE OF REFLECTION

  6. REFRACTION THE REACTION OF LIGHT WAVES WHEN THEY ENCOUNTER A TRANSPARENT INTERFACE θ1=θ2 WHERE: θ1IS THE ANGLE OF INCIDENCE θ2IS THE ANGLE OF REFRACTION THE LIGHT RAY BENDS TOWARD THE NORMAL LINE IF IT GOES INTO AN OPTICALLY MORE DENSE MEDIUM (THE VELOCITY OF LIGHT IS SLOWER)

  7. TOTAL INTERNAL REFLECTION • WHEN LIGHT TRAVELS INTO AN OPTICALLY LESS DENSE MEDIUM IT WILL BEND AWAY FROM THE NORMAL LINE • θ1 = θC (THE CRITICAL ANGLE) WHEN θ2 = 90o • IF θ1>θc THERE WILL BE NO REFRACTED WAVE • THE TRANSPARENT INTERFACE WILL BEHAVE AS A PERFECT MIRROR

  8. PRISM AS A MIRROR • THE ADVANTAGE OF USING A PRISM AS A MIRROR IS THAT THE REFLECTING SURFACE CANNOT GET DIRTY

  9. PRISMS IN BINOCULARS • PRISMS ARE USED IN BINOCULARS TO • INVERT THE IMAGE • LENGTHEN THE “TELESCOPE” TO GET GREATER MAGNIFICATION

  10. DIFFRACTION • THE BENDING OF A WAVE WHEN IT ENCOUNTERS AN OBSTACLE

  11. DISPERSION USING VARIABLE REFRACTION • DISPERSION IS THE SPREADING OF LIGHT INTO ITS COMPONENT COLORS • IN A PRISM BLUE LIGHT IS DISPERSED (BENT) MORE THAN RED LIGHT

  12. PRISM SPECTROGRAPH • THE ENTRANCE SLIT NARROWS THE LIGHT WAVES BEING CONSIDERED • ALL THE LIGHT OF A GIVEN WAVELENGTH (COLOR) IS FOCUSED AT THE SAME SPOT ON THE FILM • BLUE LIGHT IS BENT MORE THAN RED LIGHT • THERE WILL BE AN IMAGE OF THE ENTRANCE SLIT FOR EACH COLOR THAT IS IN THE SOURCE. • HENCE THE TERM “SPECTRAL LINE”

  13. GRATING SPECTROGRAPH • DISPERSION IS ACCOMPLISHED BY DIFFRACTION AND INTERFERENCE • RED LIGHT IS BENT MORE • THE ZERO ORDER IS CALLED THE “WHITE” FRINGE • HIGHER ORDERS ARE DISPERSED MORE (THE SPECTRAL LINES ARE FARTHER APART)

  14. RESOLUTION (RESOLVING POWER) • RESOLUTION (α), THE MINIMUM ANGLE BETWEEN TWO OBJECTS SUCH THAT THEY CAN JUST BE DISTINGUISHED • SINCE THE MINIMUM ANGLE IS SUBJECTIVE, LORD RAYLEIGH DEFINED IT TO BE WHERE THE AIRY DISKS OF ADJACENT STAR IMAGES OVERLAPPED AT “HALF POWER” • THEN THE EXPRESSION FOR THE RESOLUTION BECAME: α(arcsec) = 250,000 λ/a • NOTE: HIGH RESOLUTION CORRESPONDS TO SMALL α • TO MAKE α SMALL EITHER λ MUST BE SMALL OR a MUST BE LARGE • THAT’S WHY LARGER TELESCOPES HAVE HIGHER RESOLUTION

  15. THE AIRY DISK

  16. SPHERICAL LENS

  17. CHROMATIC ABERRATION

  18. SPHERICAL ABERRATION

  19. COMPOUND LENSES • ACHROMATIC DOUBLET – TWO LENSES MADE OF DIFFERENT TYPES OF GLASS (HAVING DIFFERENT INDICES OF REFRACTION) • THE INDEX OF REFRACTION IS THE VELOCITY OF LIGHT IN FREE SPACE DIVIDED BY THE VELOCITY OF LIGHT IN THE MEDIUM. • YOU CAN CHOOSE TWO WAVELENGTHS (COLORS) WHICH FOCUS AT THE SAME PLACE • IF YOU USE THREE LENSES YOU CAN CHOOSE THREE WAVELENGTHS THAT FOCUS AT THE SAME PLACE • IN ANY MULTIPLE LENSE ARRANGEMENT YOU CAN CHOOSE AS MANY WAVELENGTHS WHICH FOCUS AT THE SAME PLACE AS LENSES THAT YOU USE.

  20. TELESCOPE PROPERTIES • MAGNIFICATION (M): M = f0/fe, where f0 is the objective focal length and fe is the eyepiece focal length • SPEED (f#, f stop, focal ratio): f# = f0/a, where a is the aperture size • RESOLUTION (α), the minimum angle between two objects such that they can just be distinguished: α(arcsec) = 250,000 λ/a

  21. GALILEAN TELESCOPEVIRTUAL ERECT IMAGE – CURRENT DAY OPERA GLASSES

  22. REFRACTING TELESCOPEINVERTED IMAGE

  23. REFLECTING TELESCOPEPRIME FOCUSING SYSTEM

  24. REFLECTING TELESCOPENEWTONIAN FOCUSING SYSTEM

  25. REFLECTING TELESCOPECASSAGRAIN FOCUSING SYSTEM

  26. REFLECTING TELESCOPECOUDE’ FOCUSING SYSTEM

  27. REFLECTING TELESCOPES ADVANTAGES DISADVANTAGES SMALL FIELD OF VIEW • CAN BE TRULY PARABOLOIDAL • CAN BE MADE LARGER • ONLY ONE SURFACE TO GRIND • EASIER TO SUPPORT • FASTER (SHORTER FOCAL LENGTH)

  28. SCHMIDT CATADIOPTRIC TELESCOPEWIDE FIELD OF VIEWPRIMARY MIRROR IS SPHERICAL

  29. MAKSUTOV CATADIOTRIC TELESCOPEWIDE FIELD OF VIEWPRIMARY MIRROR IS SPHERICAL

  30. ABERRATION OF STARLIGHT • THE APPARENT CHANGE IN A STAR’S LOCATION CAUSED BY THE EARTH’S MOTION • DISCOVERED BY BRADLEY 1N 1729

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