Prozorov_30 - PHYSICS 222 Introduction to Classical Physics...

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Unformatted text preview: PHYSICS 222 Introduction to Classical Physics II Prof. Ruslan Prozorov Iowa State University Fall 2011 LECTURES 30 Optical instruments: cameras, the eye, etc. Polarization. aberrations Spherical aberration: rays far from the lens axis do not focus at the focal point Solutions: compound-lens systems; use only central part of lens Distortion: caused by variation in magnification with distance from the lens axis. Barrel and pincushion distortion: PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 2 Chromatic aberration: light of different wavelengths has different indices of refraction and focuses at different points Solution: Achromatic doublet, made of lenses of two different materials PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 3 The human eye One converging lens (crystalline) with varying f that forms images on a screen (retina). PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 4 adjusting the focal length The crystalline is flexible so that it can become thinner or thicker depending on the position of the object to be seen. Normal, healthy eye: Relaxed crystalline: f = distance to retina rays from infinity focus on retina Looking closer •Incoming rays are divergent •Need more converging power, ie, smaller f to form image on retina (“accomodation”) relaxed thicker crystalline (non-relaxed) PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 5 focal distances of an eye Far point = distance that relaxed eye can focus onto retina(∞ for normal eye) 1 f 1 2.5cm f = 1 s + = 0+ 1 s¢ 1 Þ 2.5 cm f = 2.5 cm Near point = closest distance that can be focused on to the retina (~ 25 cm for normal eye) 1 f 1 25cm f = = 1 s + 1 25 1 s¢ + 1 2.5 Þ f = 2.3 cm Diopter: 1/f Eye = 40 diopters, accommodates by about 10%, or 4 diopters PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 6 The eye—vision problems When the lens of the eye allows incoming light to focus in front of or behind the plane of the retina, a person’s vision will not be sharp. PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 7 nearsighted eyes Parallel rays converge in front of the retina Non-relaxed crystalline can focus closer objects. Blurry image Relaxed Non-relaxed Correction: diverging lens PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University Relaxed 4 November 2011 8 farsighted eyes Parallel rays converge behind the retina when crystalline is relaxed. Crystalline cannot make f small enough to focus on close objects. Relaxed Blurry image Non-relaxed (smaller possible f) Correction: converging lens PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University Blurry image Relaxed 4 November 2011 9 The camera PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 10 Camera A camera basically consists of a converging lens that focuses an image on the photographic plate, film or image sensor. F PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University F 4 November 2011 11 focal length and angle of view F F f1 In case 2, image is smaller F F f2 < f1 You can fit dog and surroundings on film’s surface Smaller f larger angle of view + smaller image PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 12 exposure You need enough energy to reach the film to leave a mark. • too little energy: underexposed film, weak and dark image • too much energy: overexposed film, everything looks whitish Two parameters to play with: Time: Need brief opening of shutter for moving subject, but then little light can come in. Aperture D: A diaphragm controls the effective diameter of the lens. Larger lens means more light reaching the film, but then we are moving away from the paraxial limit aberrations (image is less “sharp”) PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 13 1 1 1 di do f di f d 0 f 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 amount of light that enters the camera: D time f 2 PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University di f m do do f f number D D lens opening 4 November 2011 14 size perception Our sense of the size of an object (in the absence of other clues) is determined by the size of image on the retina. This is proportional to the angle subtended by the object: h 1 h a2 < a1 Bigger image PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University Smaller image 4 November 2011 15 simple magnifier Converging lens with object at s ≤f θout θin Angular magnification out 25 cm M in f PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 16 The microscope Optical elements are arranged to magnify tiny images for visual inspection. PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 17 microscope A compound microscope also has an objective and an eyepiece; it is different from a telescope in that the object is placed very close to the eyepiece. The magnification is given by: 25cm l f e M M e m0 f d e 0 25cm l M f e f 0 PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 18 The telescope Optical elements are arranged to magnify distant objects for visual inspection. PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 19 different telescopes astronomical terrestrial PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 20 the reflecting telescope Optical elements are arranged to reflect collected light back to an eyepiece or detector. This design eliminates aberrations more likely when using lenses. It also allows for greater magnification. PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 21 selecting one orientation of the EM wave PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 22 Polarized light y x z E-field is oriented in a particular direction (wave is said to be polarized in that direction). ˆ ˆ E (cos j sin k )E 0 cos(kx t ) E0 Natural light is unpolarized. Example: light-bulb: E-field is in random directions (the decay of excited atoms has no fixed orientation) PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 23 polarization PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 24 Polarization II PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 25 polaroid filters Polaroid sheets or filters: long molecules lined up in stretched sheets Light is sent through sheet: E-field in one direction passes through sheet PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 26 polarized light through a polarizing filter Linearly polarized light is shone on a polarizing filter. The direction of the E field makes an angle θ with the filter’s transmission axis (y direction). Only the projection of the E-field is transmitted through the filter. E y E 0 cos Transmitted light is now polarized in the direction of the filter (y). Intensity of light I E 2 For the transmitted light, E 2 E y2 E 02 cos2 I I0 cos2 Law of Malus PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 27 Unpolarized through a polarizing filter Unpolarized light is a superposition of light that is linearly polarized in random directions (between 0 and 180°). Probability that a ray has polarization between θ and θ +dθ f 1 d Transmitted intensity due to light with polarization between θ and θ +dθ I 0 cos2 dI d Overall: I0 I cos2 d 0 I 1 I0 2 PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 28 Circular and elliptical polarization Ex E0x cos(kz t x ) E y E 0 y cos(kz t y ) x y 0 y E E0y θ E 0x x tan y x y E and E 0 y E 0x x 2 x y 2 y E x and E 0 y E 0x PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University Linear polarization in direction θ Circular polarization Elliptical polarization 4 November 2011 29 Linear polarization Circular polarization Elliptical polarization PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 30 atmospheric scattering of light o The observed colors in the sky depend on the scattering phenomenon. Deep blue sky comes from preferential scattering of photons of shorter wavelength in the visible spectrum. o Clouds are white because they scatter all wavelengths efficiently. PHYS222 - Lecture 30 - Prof. Ruslan Prozorov - Iowa State University 4 November 2011 31 ...
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This note was uploaded on 11/14/2011 for the course PHYS 5863005 taught by Professor Meyer during the Fall '09 term at Iowa State.

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