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Convex & Concave Chapter 23: Geometric Optics Review Basic Geometry! Ray Approximation • The rays are straight lines perpendicular to the wave fronts • With the ray approximation, we assume that a wave moving through a medium travels in a straight line in the direction of its rays Light Rays: Ignore Diffraction and Interference of waves! Diffraction depends on SLIT WIDTH: the smaller the width, relative to wavelength, the more bending and diffraction. We will assume that λ<<d , where d is the diameter of the opening. This approximation is good for the study of mirrors, lenses, prisms, etc. Reflection & Refraction nn1sin 1 2 sin 2 ir Following the Reflected and Refracted Rays •Ray is the incident ray. •Ray is the reflected ray. •Ray is refracted into the lucite. •Ray is internally reflected in the lucite. •Ray is refracted as it enters the air from the lucite. Section 35.5 Law of Reflection • The normal is a line perpendicular to the surface – It is at the point where the incident ray strikes the surface • The incident ray makes an angle of θ1 with the normal • The reflected ray makes an angle of θ1’ with the normal Specular Reflection • Specular reflection is reflection from a smooth surface • The reflected rays are parallel to each other • All reflection in this text is assumed to be specular Diffuse Reflection • Diffuse reflection is reflection from a rough surface • The reflected rays travel in a variety of directions • A surface behaves as a smooth surface as long as the surface variations are much smaller than the wavelength of the light Law of Reflection ir Why are most materials Opaque? (Opaque – Can’t see through) They absorb light without re-emitting it. Vibrations given by the light to their atoms and molecules are turned into random kinetic energy – they become slightly warmer. Opacity: Mirrors Free electrons in opaque reflective surfaces can vibrate, absorb & re-emit at any frequency. Mirror Mirror Transparency Selective Absorption Glass resonates strongly with UV and infrared, absorbing those frequencies while transmitting visible frequencies. Refraction: Bending Light into Focus Refraction: Bending of Light Transmitted through Materials Light Bends because it Slows Down. Atoms are Optical Tuning Forks Light slows down as it travels through glass because it takes time to be absorbed and re-emitted. Light Slows Down in Materials Light Bends Toward the Normal when going from a medium of lower refractive index to one that has a higher refractive index and visa versa. lower n higher n Index of Refraction c n v n 1 Vacuum: 1 Water: 1.33 Glass: 1.46 Diamond: 2.4 The Index of Refraction • Refraction: Light Bends in Transmission • The speed of light in any material is less than its speed in vacuum • The index of refraction, n, of a medium can be defined as • For a vacuum, n = 1 speed of light in a vacuum c λ – We assume n = 1 for air n also speed of light in a medium v λ n • For other media, n > 1 λλin vacuum • n is a dimensionless number n greater than unity, not λλn in a medium necessarily an integer Some Indices of Refraction Frequency Doesn’t Change! • As light travels from one medium to another, its frequency does not change – Both the wave speed and the wavelength do change – The wavefronts do not pile up, nor are created or destroyed at the boundary, so ƒ must stay the same Snell’s Law of Refraction Angles are always measured from the normal. nn1sin 1 2 sin 2 Snell’s Law – Example Light is refracted into a crown glass slab. n1 = 1.00 and n2 = 1.52 o If θ1 = 30.0 , θ2 = ? -1 o θ2 = sin (n1 / n2) sin θ1 = 19.2 The ray bends toward the normal, as expected because n2 > n1 Snell’s Law of Refraction In general: nn1 1 2 2 nn1sin 1 2 sin 2 n1 21 n2 If nn2 1, then 1 2 measured from the normal! Prelab Emerging Beam is Parallel to Incident Beam but offset distance d, called the Lateral Shift and is the subject of this week’s lab! Fig. 35-15, p. 989 Following the Reflected and Refracted Rays •Ray is the incident ray. •Ray is the reflected ray. •Ray is refracted into the lucite. •Ray is internally reflected in the lucite. •Ray is refracted as it enters the air from the lucite. Section 35.5 Beam & Refraction Directions • Possible directions of the beam are indicated by rays numbered 1 through 5 • The refracted rays are bent away from the normal since n1 > n2 Total Internal Reflection 2 90 nnsin sin 1n 1 2 2 2 The Critical Angle sinC n1 Critical Angle • There is a particular angle of incidence that will result in an angle of refraction of 90° – This angle of incidence is called the critical angle, θC n2 sin θC (for n12 n ) n1 • An application of internal Fiber Optics reflection • Plastic or glass rods are used to “pipe” light from one place to another • Applications include: – medical use of fiber optic cables for diagnosis and correction of medical problems – Telecommunications • A flexible light pipe is called an optical fiber • A bundle of parallel fibers (shown) can be used to construct an optical transmission line Critical Angle Sample Problem A ray of light, emitted by a laser located beneath the surface of an unknown liquid with air above it, undergoes total internal refection as shown. What is the index of refraction for the liquid? What is its likely identification? If you pass white light through a prism, it separates into its component colors. long wavelengths short wavelengths R.O.Y. G. B.I.V The index of refraction depends on WAVELENGTH. long wavelengths short wavelengths R.O.Y. G. B.I.V The speed and wavelength change but the FREQUENCY does NOT. Fr Frequency depends on the oscillating source! long wavelengths short wavelengths R.O.Y. G. B.I.V Why does Violet Light bend more than Red Light? Violet light slows down more because the atoms in the material are tuned to higher frequencies. As the violet light travels through glass it takes more time to be absorbed and re-emitted. Variation of Index of Refraction with Wavelength speedof light ina vacuum c λ n speedof light inamedium v λn • This dependence of n on λ is called dispersion • The index of refraction for a material generally decreases with increasing wavelength • Violet light bends more than red light when passing into a refracting material Refraction in a Prism •Since all the colors have different angles of deviation, white light will spread out into a spectrum. – Violet deviates the most. – Red deviates the least. – The remaining colors are in between. Section 35.7 Dispersion via Diffraction constructive: dsin m , m 0,1,2,3 If you pass white light through a prism, it separates into its component colors. long wavelengths short wavelengths R.O.Y. G. B.I.V The index of refraction depends on WAVELENGTH. long wavelengths short wavelengths R.O.Y. G. B.I.V The speed and wavelength change but the FREQUENCY does NOT. Fr Frequency depends on the oscillating source! long wavelengths short wavelengths R.O.Y. G. B.I.V Why does Violet Light bend more than Red Light? Violet light slows down more because the atoms in the material are tuned to higher frequencies. As the violet light travels through glass it takes more time to be absorbed and re-emitted. Variation of Index of Refraction with Wavelength speedof light ina vacuum c λ n speedof light inamedium v λn • This dependence of n on λ is called dispersion • The index of refraction for a material generally decreases with increasing wavelength • Violet light bends more than red light when passing into a refracting material Angle of Deviation • Since all the colors have different angles of deviation, white light will spread out into a spectrum – Violet deviates the most – Red deviates the least – The remaining colors are in between Dispersion Sample Problem The index of refraction for violet light in silica flint glass is 1.66, and that for red light is 1.62. What is the angular nn1sin 1 2 sin 2 dispersion of visible light passing through a prism of apex angle 60.0° if the angle of incidence is 50.0°? red (660 nm) violet (410 nm) Use Snell’s Law twice and some geometry! Angles are always measured from the normal. Thin Film Interference Interference in Thin Films When reflecting off a medium of greater refractive index, a light wave undergoes a phase shift of ½ a wavelength. Wave 1 undergoes a phase shift of 180 degrees. From Low to High, a phase change of pi! From High to Low, a phase change? NO! Interference in Thin Films • The wavelength of ray 1 in the film is /n • For constructive interference 2t = (m + ½) /n (m = 0, 1, 2 …) This takes into account both the difference in optical path length for the two rays and the 180° phase change • For destructive interference 2t = m/n (m = 0, 1, 2 …) Problem: Thin Films A thin film of gasoline floats on a puddle of water. Sunlight falls almost perpendicularly on the film and reflects into your eyes a yellow hue. Interference in the the thin gasoline film has eliminated blue (469nm in vacuum) from the reflected light. The refractive indices of the blue light in gasoline and water are 1.40 and 1.33 respectively. Determine the minimum nonzero thickness of the film. What color do you see? Thin Film Interference The light reflected from a soap bubble (n = 1.40) appears red ( = 640 nm).
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