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

ELECTROMAGNETIC WAVES

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

LONGITUDINAL WAVES

• PARTICLE MOTION IS PARALLEL TO THE WAVE DIRECTION

• EXAMPLE – SOUND WAVES

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)

REFLECTION

• REACTION OF LIGHT WAVES WHEN THEY ENCOUNTER AN OPAQUE MEDIUM

i=rWHERE:i IS THE ANGLE OF INCIDENCE

r IS THE ANGLE OF REFLECTION

REFRACTION

THE REACTION OF LIGHT WAVES WHEN THEY ENCOUNTER A TRANSPARENT INTERFACE

θ1=θ2

WHERE:θ1 IS THE ANGLE OF INCIDENCE

θ2 IS 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)

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

PRISM AS A MIRROR

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

PRISMS IN BINOCULARS

• PRISMS ARE USED IN BINOCULARS TO– INVERT THE IMAGE– LENGTHEN THE

“TELESCOPE” TO GET GREATER MAGNIFICATION

DIFFRACTION

• THE BENDING OF A WAVE WHEN IT ENCOUNTERS AN OBSTACLE

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

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”

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)

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

THE AIRY DISK

SPHERICAL LENS

CHROMATIC ABERRATION

SPHERICAL ABERRATION

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.

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

GALILEAN TELESCOPEVIRTUAL ERECT IMAGE – CURRENT DAY OPERA GLASSES

REFRACTING TELESCOPEINVERTED IMAGE

REFLECTING TELESCOPEPRIME FOCUSING SYSTEM

REFLECTING TELESCOPENEWTONIAN FOCUSING SYSTEM

REFLECTING TELESCOPECASSAGRAIN FOCUSING SYSTEM

REFLECTING TELESCOPECOUDE’ FOCUSING SYSTEM

REFLECTING TELESCOPESADVANTAGES

• CAN BE TRULY PARABOLOIDAL

• CAN BE MADE LARGER• ONLY ONE SURFACE TO

GRIND• EASIER TO SUPPORT• FASTER (SHORTER FOCAL

LENGTH)

DISADVANTAGES• SMALL FIELD OF VIEW

SCHMIDT CATADIOPTRIC TELESCOPEWIDE FIELD OF VIEW

PRIMARY MIRROR IS SPHERICAL

MAKSUTOV CATADIOTRIC TELESCOPEWIDE FIELD OF VIEW

PRIMARY MIRROR IS SPHERICAL

ABERRATION OF STARLIGHT

• THE APPARENT CHANGE IN A STAR’S LOCATION CAUSED BY THE EARTH’S MOTION

• DISCOVERED BY BRADLEY 1N 1729