TRIVIA QUESTION! How big (diameter of largest reflective mirror) is the LARGEST telescope in the world? (a) (b) (c ) (d) 34 feet (e) Telescope, Location, Date Built Aperture Size Gran Telescopio Canarias, Canary Islands, Spain, 2009 409 inches

Diffraction through a Lens

Diffraction through a Lens do=-(z-L) di VIRTUAL object ANGULAR width of diffraction pattern at z approaching infinity and at f IS THE SAME

Diffraction through a telescope NOTE: Ray THROUGH MIDDLE of lens is NOT refracted in the thin lens approximation Images of stars no longer resolved when diffraction patterns overlap

Diffraction limits through a lens Diffraction limits your ability to resolve two sources Diffraction Limitations on Resolving Two Sources Changing an Aperture size (or size of Lens) limits the resolution of two sources. BIG telescopes are BETTER at resolving objects which are close together Diffraction Limits and Aperture Size The larger the wavelength, the lower the resolution in resolving objects – eg. Blue lasers for CD readers Diffraction Limits and Wavelength http://phys23p.sl.psu.edu/phys_anim/optics/indexer_opticsC.html

Diffraction through a telescope Use x=1.22π for first zero of First Order Bessel Function J1 to determine half width of diffraction peak

Rayleigh Criteria ρ Why is it desirable to have LARGE telescopes with LARGE diameter mirrors?

Examples of Diffraction Focusing light with a lens wo Geometric Optics – Wavelength small compared to other dimensions. No Diffraction. Light focuses to a point. Wave Optics – Wavelength can be comparable to other dimensions. Diffraction MUST be considered. Light focuses to a minimum spot size.

Gaussian Beams Polar coordinates wo is the radius at which the ELECTRIC field is reduced by 1/e or the INTENSITY is reduces by 1/e2

Gaussian Beams

Gaussian Beams Beam size ROUGHLY constant As beam size increases, intensity decreases

Gaussian Beams Max intenxity at CENTER of beam profile

Gaussian Beams Phase of CURVED wavefronts At LARGE distances (z >> zo ), radius of curvature =z. Spherical-like wave front. At MINIMUM beam waist (z=0), Radius of curvature of wavefronts goes to infinity (planar wave front)

Gaussian Beams – Gouy Phase Shift Phase shift as light goes through focus Gouy phase shift not that important at OPTICAL frequencies, but important at lower (microwave to Terahertz) since in the lower frequency ranges one can DIRECTLY measure electric