Prozorov_26 - 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 26 Geometric optics The Nature of light Index of refraction “light is a wave,” “light is a particle” It turns our EM waves can interact with matter in portions called PHOTONS. for every wavelength, there are photons with energy U and momentum p U pc hf hc hf h p k c 34 h 6.63... 10 J s = h 2 PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 2 introduction to geometric optics Select an object of your choice (table, book, coin, neighbor’s head). Think about: • what it means to “see it” EM waves (light) from lamps hit surface and are reflected. Waves propagate spherically in all directions from object. Your eye is sensitive to light • how you perceive the position of that object brain “traces back” to where the light comes from. 3D perception comes from brain comparing images from each eye. PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 3 wave fronts and rays o Light is actually a nearly uncountable number of electromagnetic wave fronts, but analysis of refraction or reflection are made possible by treating light as a ray. PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 4 light rays = Geometrical abstraction that allows us to work with the direction that an E/B wave travels Instead of drawing E/B fields, we draw a “ray” Ray : a line in the direction along which light energy is traveling PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 5 ray model of light • • • • Light travels through a transparent medium in straight lines at a speed: v =c /n (n = index of refraction) Light rays do not interact with each other A light ray continues forever unless it interacts with matter Interactions light/matter: • at an interface between two media reflected and refracted • within a medium, light can be scattered or absorbed medium 1 medium 2 reflection scattering PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University refraction absorption 24 October 2011 6 reflection and refraction • The storefront window both shows the passersby their reflections and allows them to see inside. PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 7 two types of reflection specular reflection smooth surface e.g. mirrors diffuse reflection rough surface e.g. screens PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 8 mirror reflection qi qr mirror • • Incident angle = reflected angle Always draw line that is “normal” (90°) to mirror – calculate angles with respect to this normal PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 9 image reflected on a plane mirror A book is in front of a plane mirror. If you see it through the mirror, where does it appear to be? All the reflected rays seem to be coming from here! No rays really pass behind the mirror. This is a virtual image. PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 10 how to find the image • Draw two rays (one of them the normal to the surface, it’s a trivial one) • Draw reflected rays. • Extrapolate rays until they intersect. Plane mirror: s = -s’ s s’ s : location of the object Positive in front of mirror s’: location of the image Negative behind mirror PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 11 EM waves not in vacuum E field inside a material is characterized by dielectric constant or the dielectric permittivity 0 Similarly: B field inside a material is characterized by relative permeability m or the permeability 0 EM wave speed in general: v 1 c m c n PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University n m 1 always Refraction index 24 October 2011 12 refraction Fact: Light changes direction when it crosses a boundary Reason: Speed of light is different in both media – At boundary, part of wavefront is in slower media – Travels shorter distance in Dt slower PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 13 why should the ruler appear to be bent? o The difference in index of refraction for air and water causes your eye to be deceived. Your brain follows rays back to the origin they would have had if not bent. PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 14 laws of reflection and refraction o Angle of incidence = angle of reflection. o Snell’s Law of Refraction considers the slowing of light in a medium other than vacuum … the index of refraction. PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 15 exam problem: refraction A ray of light strikes the interface between air and an unknown substance at an angle θ1 = 75° from the normal to the surface. The refracted beam makes an angle θ2 = 30° from the normal. What is the index of refraction of this substance? A. 2.5 75° 75° B. 1.9 air X C. 1.3 30° D. 1.0 E. 0.50 Impossible, n 1 = 1.0 nair sin75 nX sin30 sin 75 nX 1.9 sin30 PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 16 example: angle of refraction If n1 > n2 , which direction does the ray go? n1 n2 1 2 n1 sin q1 n2 sin q2 3 PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University n1 sin q2 sin q1 sin q1 n2 q2 q1 Remember: angles defined with respect to normal! 24 October 2011 17 exam problem: angle of refraction • - When it re-emerges into medium 1, the direction of the ray is: n1 sin q1 n2 sin q2 n1 sin q1 • - n1 q1 q1 q1 • - It comes out exactly parallel to the original ray. q2 n2 q2 47% 33% 20% PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 1 2 n1 q1 3 24 October 2011 18 why should sunsets be orange and red? o The light path at sunset is much longer than at noon when the sun is directly overhead PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 19 some indexes of refraction PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 20 total internal reflection As light goes to a medium with lower n, the angle from the normal increases (θ1 < θ2): q1 n1 n2 < n1 q2 q1 q2 q1c q1 q2 If θ1 is large enough, θ2 = 90° !! Beyond this angle, there is no more refraction, only reflection. PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 21 total internal reflection o As the angle of incidence becomes more and more acute, the light ceases to be transmitted, only reflected PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 22 total internal reflection PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 23 total internal reflection o Diamonds sparkle as they do because their index of refraction is one of the highest a transparent material can have. Nearly all light that enters a surface ends up making many passes around the inside of the stone. The effect is only amplified by cutting the surfaces at sharp angles. PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 24 the critical angle =1 n1 sin q1c n2 sin90 q1c n2 sin n 1 1 PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University q1c n1 n2 < n1 q2 90 24 October 2011 25 fiber optics cladding core Both cladding and core are glass such that ncore > ncladding Light internally reflects within the inner glass fiber – no refracted ray going outside – minimal light loss PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 26 road mirages PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 27 road mirages Hot air lower density lower n High n Total internal reflection Low n Hot road Image of sky on the road (that brain interprets as water to explain “reflection”) PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 28 light through matter: a simple model What does really happen when light travels through matter? It depends on how you want to think about it. atom You can say that the photons occasionally interact with atoms in a dielectric, being absorbed and re-emitted, and that this only appears to slow them down. Here, the photons travel at “c”. v=c v=c absorb & re-emit with some phase delay Or you can say that the wave that propagates through the solid is a combination of a photon and virtual excitations of the atoms of the solid. This wave travels with v < c. PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 29 what defines a color? So the atom oscillates with the frequency of the radiation and then re-emits. Frequency remains the same Wavelength changes n1 v1 c 1 f n1f n2 < n1 v2 c 2 1 f n2f “Color” correspond to a fixed frequency. The wavelength depends on the medium. PHYS222 - Lecture 26 - Prof. Ruslan Prozorov - Iowa State University 24 October 2011 30 ...
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