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Friday lunchtime was the equinox. Which of the following will NOT happen between now and Mid June? A. B. C. D. Earth will get closer to the Sun The North Pole will tilt toward the sun Winter will arrive in Chile The south pole will get less daylight Lecture 15 Applications in Optics (Giancoli Chapter 23/25) What is this picture? A. Map of the early universe in Polarized light B. Graph of the stress in a piece of glass using polarized light C. Plot of the optical aberrations in a human eye Human Vision Contact lenses & eyeglasses Cameras Telescopes Microscopes Refraction Spectrographs Dispersion Liquid Crystal Displays Diffraction Antireflection coatings Polarization X-ray “optics” Lenses Mirrors Focal Length Magnification Polarization • Light is polarized when its electric fields oscillate in a single plane. • Consequence of the direction of oscillation of electrons in atoms • Light gets polarized when it reflects off surfaces, or is scattered by gases (e.g. the atmosphere) • Any electromagnetic wave can be polarized. • Another important example is radio waves. • Can sound waves be polarized? Polarizing Filters (polaroid) • Polarized light will not be transmitted through a polarized film whose axis is perpendicular to the polarization direction. • Polarizing filters are used in Photography, Sunglasses, Science Labs etc. • Usually created by stressing plastics while they are still partially melted, creating a preferred direction of vibration for the molecules. Transmitted Blocked Many Car windows show a pattern when viewed though polarized sunglasses. The glass contains stresses created by heating and cooling. It is designed to shatter into tiny pieces in an accident, instead of sharp shards that could cut people . The stresses give the glass molecules preferred directions of oscillation, hence they act as a polarizing filter. Crossed Polarizers If initially unpolarized light passes through crossed polarizers, no light will get through the second one. This can be very useful, as certain special materials can rotate the plane of polarization. Polarization When light passes through a polarizer, only the component parallel to the polarization axis is transmitted. If the incoming light is planepolarized, the outgoing intensity is: You are looking through a single polarizer at an unpolarized light. What angle do you need to rotate a second polarizer (relative to the first) in order to block half of the remaining light? A. B. C. D. 0 degrees 30 degrees 45 degrees 90 degrees Polarization upon Reflection • Light is also polarized after reflecting from a nonmetallic surface. • At a special angle, called the polarizing angle or Brewster’s angle, the polarization is 100%. • Reflected Light is Horizontally Polarized • Incident waves that are vertically polarized get absorbed and so are not reflected (24-6a) For light in air, reflecting off water, Brewster’s angle is 53 degrees Use of Polarizer to remove Reflections and Glare in Photography (and Everyday life) Without polarizer: (or adjusted horizontally) Reflections in surface of water With Polarizer: (adjusted vertically) Reflections suppressed. The leaves at the bottom of the pond are now visible Polarization of rainbows • Rainbows involve reflection and refraction both inside and at the boundaries of the raindrops. • The rainbow is 100% linearly polarized • The polarization axis is radial to the bow • Just rotate your head while wearing polarized sunglasses Why is the Sky Blue? and is it also Polarized? • The clear sky is blue due to Scattering by air molecules. • Scattering is a directional process. • Examine the sky with polarized sunglasses! • At 90 from the Sun, the polarization is upto 80%. -so it will look dark! The blue sky is polarized Rotating your polarized sunglasses will show regions of light and dark in the sky, that change depending on where you look. Light from other objects in the sky are mostly not polarized and so the moon, planets and brighter stars can sometimes be seen in datytime using this trick. The polarization pattern is quite striking • • • • Polarization of the sky reaches its maximum strength at 90 degrees from the sun Go see if you can observe the overall pattern for yourself Its very hard to photograph! The Sun is hidden behind a streetlamp in this photo (I had to crouch dwn and position the camera very carefully!) Map of the polarization pattern in the Cosmic Microwave Background • • • • • Found by the South pole telescope and announced this week! It confirms a strange and ridiculously specific prediction of the Big Bang theory The most significant cosmological discovery in a generation ? It looks a lot like a car window viewed though a polarizer The “stress” pattern in this case was imprinted by gravitational waves during the earliest moments of the big bang South Pole Telescope Liquid Crystal Displays (LCD) Color LCD displays are more complicated; each pixel has three subpixels to provide the different colors. A source of light is behind the display (unlike calculators and watches, which use ambient light). The pixels must be able to make finer adjustments than just on and off to provide a clear image. 25.1 Cameras, Film, and Digital A digital camera uses CCD sensors instead of film. The digitized image is sent to a processor for storage and later retrieval. Cameras, Film, and Digital Basic parts of a camera: • Lens • Light-tight box • Shutter • Film or electronic sensor Cameras, Film, and Digital There is a certain range of distances over which objects will be in focus; this is called the depth of field of the lens. Objects closer or farther will be blurred. The Human Eye The human eye resembles a (vastly more complex and sophisticated) camera in its basic functioning, with its adjustable lens, iris (aperture), and retina (detector). The Human Eye; Corrective Lenses Nearsightedness can be corrected with a diverging lens. And farsightedness with a converging lens. Underwater vision and goggles Vision is blurry underwater because light rays are bent much less than they would be if entering the eye from air. This can be avoided by wearing goggles. Why is it that when you open your eyes under water (with no goggles!), everything is Blurry? A. Your eyes cannot focus under water B. The refractive index of water is similar to that of your eye’s lens. C. The water is rippling, blurring the view D. It stings, so you never noticed! A nearsighted person requires what type of lenses In their eyeglasses or contact lenses ? A. B. C. D. Converging Diverging Depends on their prescription Neither Limit of Resolution: Diffraction • Resolution is the smallest separation (or angle) at which a lens can barely distinguish two separate objects. • Resolution is limited by aberrations and by diffraction. • Aberrations can be minimized. • Diffraction is unavoidable; it is due to the size of the lens compared to the wavelength of the light. Limit of Resolution for Circular Apertures For a circular aperture of diameter D, the central maximum has an angular width: Rayleigh Criterion, or the Diffraction Limit The Rayleigh criterion states that two images are just resolvable when the center of one peak is over the first minimum of the other. • The chief practical implication of Rayleigh’s Criterion, is that ANY optical device (eye, camera, telescope, radio-telescope etc) cannot resolve details finer than θ (in radians) = 1.22λ/D. Where D is the diameter (in meters) of the objective lens or mirror, and λ the wavelength (in meters) of the light in question. • Similarly, light emitted from an aperture D will spread out with this angle (θ), due to diffraction. Even if the light rays start out perfectly parallel! • Thus, the Wider the Aperture, the Sharper the Image. Remember this! What is the smallest detail on the Earth’s surface that can be made out in photos taken by a camera with a 2.3m diameter objective mirror, carried by on a satellite in near earth orbit? The Hubble Space Telescope (diameter 2.3 m is similar to the imaging satellites flown by the National Reconnaissance Office (NRO), except they look DOWN! What’s the smallest detail the human eye can see at a distance of: • • • • • • 20 cm? 1 meter ? 10 meters 1 km? 100 km ? 500,000 km ? Why can’t we see bacteria without a microscope? Why can’t you recognize people a mile away? Spherical Aberrations of Lenses Spherical aberration: rays far from the lens axis do not focus at the focal point. Solutions: compound-lens systems (camera lenses can have > 15 elements!) use only central part of lens (e.g. by stopping it down) Aspherical lens surfaces (expensive to produce) Aberrations of Lenses and Mirrors Geometric Distortion: caused by variation in magnification with distance from the lens. Barrel and pincushion distortion: Solutions: multiple elements, aspheric curves, stopping down, image processing Chromatic Aberration Light of different wavelengths has different indices of refraction and focuses at different points Solutions: Use only the center, stop down, use very long focal length, use colored filters, use multiple lenses The Achromatic Doublet • Achromatic doublet is a lens made of two lenses of different glass types that have different amounts of dispersion. • Usually a Strong Converging lens made from a low dispersion glass, is glued to a Weaker Diverging lens (made from a higher dispersion glass) • The space between can be filled with glue, or oil. • Anti-reflection coatings are required to prevent “ghost” images forming Refracting Telescopes • Refractors consist of an objective lens and an eyepiece lens. • Naturally produce upside down images • A terrestrial telescope, used for viewing objects on Earth, should produce an upright image. • Here are two models, a Galilean type and a spyglass: What is the magnification of a telescope (f=1000mm) when used with a 25mm eyepiece ? A. -40 B. 250 C. -500 D. 1000 Reflecting Telescopes • Astronomical telescopes need to gather as much light as possible. • And obtain the sharpest view possible. • The objective must be as large as possible. • Mirrors are now used instead of lenses, as they can be made much larger. • Mirrors focus all wavelengths of light equally (no chromatic aberration) Newtonian Cassegrain Gemini telescope objective mirror is 8 meters in diameter. The next generation will be 30 m !