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Physics 272 April 30 Spring 2015 www.phys.hawaii.edu/~philipvd/pvd_15_spring_272_uhm go.hawaii.edu/KO Prof. Philip von Doetinchem [email protected] PHYS272 - Spring 15 - von Doetinchem - 220 Thin lenses http://phet.colorado.edu/en/simulation/geometric-optics ● ● ● Object further away than focal point: – light rays converge and form a real image on the other side of the lens Object inside focal point: – Light rays diverge and the image is virtual and larger than the object Photography: having the sensor at the right focal point is essential for a sharp image PHYS272 - Spring 15 - von Doetinchem - 221 The Lensmaker's equation ● ● The image of the first refracting surface is used as the object position for the second refracting surface The sketch shows a distance of d between the two spherical mirrors → we will set distance to zero PHYS272 - Spring 15 - von Doetinchem - 222 The Lensmaker's equation ● ● Image position after the first surface: Image of first surface acts as object for second surface. In coming light on second surface is on the opposite side as the image from surface 1: s2=-s1' PHYS272 - Spring 15 - von Doetinchem - 223 The Lensmaker's equation ● Combining both equations: ● For a lens in air (s1→s, s'2→s', nb = n) PHYS272 - Spring 15 - von Doetinchem - 224 The Lensmaker's equation ● ● Focal length on both sides of the object are the same (set object distance and image distance to infinity): Be careful: rays at larger distance from optic axis are not going to the same focus point → abberation PHYS272 - Spring 15 - von Doetinchem - 225 Diverging lenses ● Converging lens: thicker in the center than at the edges ● Diverging lens: thicker at the edges than at the center ● Parallel rays are diverged → virtual image in focal point ● For calculations: use negative focal length value for diverging lens PHYS272 - Spring 15 - von Doetinchem - 226 The Eye ● ● ● ● ● ● The eye works very much like a camera Crystalline index of refraction has index of refraction of ~1.437 Eye is filled with substance having similar optical properties as water (n=1.336) Muscles change the focal length of the eye by squeezing the lens → radius gets smaller Relaxed eye focuses on infinity Image is projected in retina → connects over optic nerve to brain PHYS272 - Spring 15 - von Doetinchem - 229 Defects of vision PHYS272 - Spring 15 - von Doetinchem - 230 Correcting for farsightedness ● ● How to correct the near point of a farsighted eye from 100cm to 25cm (standard value) using a contact lens? → form a virtual image of the object at 100cm: Prescriptions typically use the inverse of the focal length → a converging lens of +3.0 diopters would correct this eye PHYS272 - Spring 15 - von Doetinchem - 231 Correcting for nearsightedness PHYS272 - Spring 15 - von Doetinchem - 232 Telescopes ● Telescopes are used to magnify objects at large distances ● Objective lens forms a real, reduced image of the object on the sky ● Objects are very far → image nearly perfectly at focal point ● first image serves as object for the eyepiece lens → if at focal point of eyepiece → observer can see the magnified virtual object at infinity PHYS272 - Spring 15 - von Doetinchem - 234 Telescopes: Hubble in space ● ● large magnification requires a large focal length f1 large focal length → lower intensity → large collecting area needed ● modern telescopes are reflecting telescopes ● Astronomy in space is great, but: – expensive – limited in size/weight → intensity limitation – very limited excess for upgrades PHYS272 - Spring 15 - von Doetinchem - 235 ● ● ● Mauna Kea's is one of the best sites in the world for astronomical observation – high altitude → less atmosphere is shielding light from stars – atmosphere above the volcano is extremely dry (water vapor absorbs radiation) → important for near-ultraviolet to mid-infrared observations – most cloud cover below the summit, free of atmospheric pollution – summit atmosphere is exceptionally stable – very dark skies (very little light pollution from the surrounding area) TMT provides: – 9 times the collecting area of the current largest optical/IR telescopes – spatial resolution 12.5 times sharper than the Hubble Space Telescope – 3 times sharper than the largest current-generation O/IR telescopes Primary goals: – explore first sources of light in the very young universe – explore galaxies and large-scale structure in the young universe – investigate massive black holes → super massive black holes are at the centers of most or all large galaxies – explore planet-formation and the characterize extra-solar planets secondary mirror Courtesy TMT International Observatory Courtesy TMT International Observatory Telescopes: Thirty Meter Telescope tertiary mirror scientific instrument primary mirror PHYS272 - Spring 15 - von Doetinchem - 236 Observation power of a big telescope credit: F.Marchis ● ● Simulation of observation of volcanic eruptions on Jupiter moon Io: – using the current Keck telescope (spatial resolution: 140km) – upgraded Keck (spatial resolution: 110km) – Thirty Meter Telescope (spatial resolution: 35km) → two young eruptive centers labeled A & B can be detected only on the TMT observations The arrival of the TMT will provide an increase in angular resolution but also in sensitivity allowing astronomers to detect fainter and smaller eruptions. PHYS272 - Spring 15 - von Doetinchem - 237 Additional Material PHYS272 - Spring 15 - von Doetinchem - 238 Image formation by a concave mirror ● Mirror radius and focal length: ● Magnification: Source: http://en.wikipedia.org/wiki/Parabolic_mirror PHYS272 - Spring 15 - von Doetinchem - 239 Image formation by refraction ● Small image in front of a cylindrical glass rod: ● image is inverted and reduced in size PHYS272 - Spring 15 - von Doetinchem - 240 Image formation by refraction ● Immerse glass rod in water (n=1.33): ● the refracted rays do not converge ● ● ● and appear to diverge from a point 21.3cm to the left from the vertex The result is a virtual image Image is still erect and the virtual image appears magnified PHYS272 - Spring 15 - von Doetinchem - 241 ● ● ● ● Converging lens in front of light detector (film or chip) Lens forms an inverted image on the light detector Magnification for object at 5m Cameras: magnification Focal length [mm] Good lenses correct for paraxial approximation and dispersion Longer focal length → higher absolute magnification factor (still inverted) → image size on light detector increases PHYS272 - Spring 15 - von Doetinchem - 242 Cameras: intensity ● ● ● Light intensity on the detector depends on field of view and the aperture opening Field of view scales roughly as 1/f2 Wide aperture allows more light to enter ● Adjusting is a typical function of cameras ● Eventually also the exposure time is adjusted PHYS272 - Spring 15 - von Doetinchem - 243 Cameras: zoom ● ● Combination of movable converging and diverging lens make it possible to change the focal length Real zoom lenses are more complicated than that and use more than 10 lenses to correct for various aberrations PHYS272 - Spring 15 - von Doetinchem - 244 Cameras: depth of focus small aperture ● large aperture Introducing an adjustable lens aperture helps increasing the depth of focus: – light rays coming from an object further away from a lens are less refracted than light rays from a closer object – Extended objects along the optic axis are in focus for a narrow (wide) region for large (small) apertures PHYS272 - Spring 15 - von Doetinchem - 245 Cameras: depth of focus large aperture short depth of field object circle of confusion Out of focus: image becomes blurry ● The circle of confusion on the image side is the size when the objects starts to appear blurry (typical: 1 pixel of the sensor) ● long depth of field object small aperture circle of confusion http://graphics.stanford.edu/courses/cs178/applets/dof.html PHYS272 - Spring 15 - von Doetinchem - 246 Cameras: autofocus ● Different autofocus techniques are available – Contrast detection – Assist lamp – Phase detection: ● ● ● ● Splits incoming light Analyzes different parts projected on different sensors in the same plane Chip compares intensity patterns Sensor plane is in focus when patterns are the same Source: http://en.wikipedia.org/wiki/Autofocus PHYS272 - Spring 15 - von Doetinchem - 247 The magnifier ● ● ● Size of an image depends on size on retina Moving object closer than near point does not help → eye cannot focus Converging lens: – Place object at focal point – Virtual image at infinity has a much larger angular size – Lateral magnification for virtual image at infinity is not a useful quantity PHYS272 - Spring 15 - von Doetinchem - 248 The microscope ● ● ● ● Image of one lens can be used as an object for the second lens → greater magnification can be reached without making the lenses too big Objects are placed closely to the focal point Short focal length of the objective and eyepiece lens cause a greater magnification Overall magnification is composed of lateral and angular magnification PHYS272 - Spring 15 - von Doetinchem - 249