Phys 322 Lecture 16 Chapter 5 Geometrical Optics Optical systems
Magnifying glass Purpose: enlarge a nearby object by increasing its image size on retina Requirements: Image should not be inverted Image should be magnified Rays entering eye should not be converging Use positive lens and s o < f
Magnifying glass Magnifying power MP, or angular magnification - the ratio of the size of the retinal image as seen through the instrument to that as seen by bare eye at a normal viewing distance: MP a u a - aided, u - unaided Largest image without aid: Standard observer: d o =0.25 m Near point, d o : closest point at which image can be brought into focus
Magnifying glass MP a u a y i / u o L y / d o unaided view aided view Using paraxial approximation and lens equation (page 211): do MP 1 D L l L MP D L d o D Most common case: s o =f, L= Standard observer: d o =0.25 m 1 f If D=10, MP=2.5, notation 2.5X Typically limited to 2.5X - 3X
Eyepiece (ocular) Eyepiece is essentially a magnifying glass that is designed to magnify image created by the previous optical system. Virtual object! Virtual image at Center of exit pupil - at eye plane The Huygens eyepiece More complex:
Microscopes Objective Image plane #1 Eyepiece Image plane #2 M 1 M 2 Microscopes goal: to magnify objects that are really close. When two lenses are used, it s called a compound microscope.
Compound microscope ~1595, Zacharias Janssen: compound microscope ~1660, Robert Hooke s microscope, ~30X magnification ~1700, Anton Van Leeuwenhoek microscope (single lens) 270X magnification Father of microscope
Total magnification: MP = M To M Ae Compound microscope angular magnification of eyepiece Transverse magnification of objective Standard design: L = 160 mm Tube length Assuming standard tube length and standard viewing distance 25 cm: 160mm 250mm MP fo fe Respective powers are marked as 10X, 20X etc.
Compound microscope Amount of light (brightness of image) depends on numerical aperture of the objective: NA = n i sin max Power = 40X NA=0.65 Maximum NA in air is 1 Can be as large as 1.4 - in oil
Microscope summary
If all light rays are directed through a pinhole, it forms an image with an infinite depth of field. The pinhole camera Object Pinhole Image The concept of the focal length is inappropriate for a pinhole lens. The magnification is still d i /d o. The first person to mention this idea was Aristotle. With their low cost, small size and huge depth of field, they re useful in security applications.
Camera obscura Latin: dark room pinhole camera 1769 Portable tent version 1620 Inside camera obscura Central Park, 1877 http://www.acmi.net.au/aic/camera_obscura.html 1665:Vermeer The Girl with the Red Hat Probably used camera obscura
Camera 1826: First photograph by Joseph Nicephore Niepce Exposure time: 8 hours!
Photography lenses Photography lenses are complex! Especially zoom lenses. Double Gauss Petzval These are older designs.
Photography lenses Modern lenses can have up to 20 elements! Canon 17-85mm f/3.5-4.5 zoom Canon EF 600mm f/4l IS USM Super Telephoto Lens 17 elements in 13 groups $12,000
Modern SLR Camera single lens reflex For sharp image lens is moved back and forth - changing s i changes s o Film size is fixed (field stop) - changing f can change angular field of view. f=6-40 mm - wide-angle f~50 mm - normal angle f=80-1000 - telephoto lens Diaphragm=variable aperture stop controls f-number, or amount of light
Telescopes Keplerian telescope A telescope should image an object, but, because the object will have a very small solid angle, it should also increase its solid angle significantly, so it looks bigger. Image plane #1 Image plane #2 M 1 M 2
The telescope tele-skopos (Greek) - seeing at a distance 1608, Hans Lippershey tried to patent kijker looker (Dutch) 1609: Galileo, two lenses and an organ pipe
Telescope Terminology
Refracting telescope Notes: image is inverted object is typically at infinity Angular magnification: MP a u f f o e
Terrestrial (non-inverting) telescope
Binoculars
Telescope aperture Telescope aperture: * determines amount of light collected more light - more low-brightness distant stars could be seen * determines the angular resolution diffraction limited angle is 1.22 /D radians (chapter 10) - wavelength of light D - diameter of lens (or mirror)
Exercise A friend tells you that the government is using Hubble telescope to read car license plates. Is it possible? Orbit height 600 km, aperture 2.4 m Hubble Assume best case scenario: the car s license plate faces up Solution: To resolve license plate number need ~2 cm resolution cm 600,000 m 2 1.22 500 nm must have D 20 m D 2.4 m telescope could resolve ~15 cm Note: atmospheric turbulence will most probably lower the resolving power below theoretical limit
Refracting telescope aperture Largest refracting telescope (~1900): 40 doublet, 500 pounds. Net weight: 20 tons Yerkes, Williams Bay, WI http://www.wavian.com/aip/cosmology/tools/tools-refractors.htm Lens versus mirror: - harder to make (need large diameter to collect more light) - focal length depends on wavelength: n=n( )
Reflecting telescopes Keck 10 m telescope Hawaii, 1993 Arecibo Observatory 305 m radio telescope
Reflecting telescope prime focus 1661: Invented by Scottsman James Gregory 1668: Constructed successfully by Newton Newtonian telescope
The Cassegrain Telescope Telescopes must collect as much light as possible from the generally very dim objects many light-years away. It s easier to create large mirrors than large lenses (only the surface needs to be very precise). Object It may seem like the image will have a hole in it, but only if it s out of focus.
Liquid mercury telescope z Liquid mercury mirror 3m NASA s Debris Observatory Spinning liquid in equilibrium: parabolic surface 2 2 r z 2g One turn in ~10 seconds must be maintained at 10-6 level ~30 L of Hg for 6 m mirror Surface smoothness ~10-7 (.3mm bump on Earth) Points only up Costs $1M instead of $100M r
6 m liquid mercury telescope f/1.5 Zenith telescope 70 km East of Vancouver f/1.5, f=10 m mirror support http://www.astro.ubc.ca/lmt/lzt/gallery.html
Correcting aberrations Spherical mirrors do not work: spherical aberrations and coma Aplanatic reflectors: Both primary and secondary mirrors are hyperbolic Example: Hubble telescope Catadioptric systems: Correct spherical aberrations using specially profiled lens
Wavefront shaping Lenses, mirrors - reshape wavefronts, designed to work with spherical or plane waves More complex elements - more complex wavefronts Phys 322 Lecture 16 Wavefront distortions Light from star passes turbulent air - wavefront is not plane anymore, it has few m distortions (> ~0.5 m) In a good night, the planar area of the wave from distant star is ~20 cm - no matter how large the telescope is resolution is the same as that of 20 cm telescope! Need techniques that could constantly adapt optical elements to restore plane wave: Adaptive optics
Adaptive optics
Phase conjugation If we could at the same instant turn the wave direction backwards we can restore the initial (plane) wave shape The light propagation is reversible. 1972: Zeldovich et al. Use Stimulated Brillouin Scattering Intense electric field increases n at minima and maxima (sound wave) - constructive backward scattering (simplified view) /2