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Geometric Optics • Ray Model • • assume light travels in straight line uses rays to understand and predict reflection & refraction General Physics 2 Geometric Optics 1 Reflection • Law of reflection • • the angle of incidence equals angle of reflection angles are measured from normal General Physics 2 Geometric Optics 2 Reflection Diffuse reflection General Physics 2 Specular reflection Geometric Optics 3 Think-Pair-Share • What would be the appearance of the Moon if it has • • (a) a rough surface? (b) a polished surface? General Physics 2 Geometric Optics 4 Plane Mirrors General Physics 2 Geometric Optics 5 Extra Credit • How large a mirror do you need to see your whole body? General Physics 2 Geometric Optics 6 Spherical Mirrors By using ray tracing and the law of reflection, you can figure out where the incoming rays are reflected. General Physics 2 Geometric Optics 7 Focal Point & Focal Length • Parallel rays striking a concave mirror come together at focal point f = r/2 r = radius of sphere f = focal length General Physics 2 Geometric Optics 8 Image Formation Real Image General Physics 2 Geometric Optics 9 Mirror Equation & Magnification General Physics 2 Geometric Optics 10 Plug & Chug • How far from a concave mirror (radius 23.0 cm) must an object be placed if its image is to be at infinity? General Physics 2 Geometric Optics 11 Convex Mirrors • Virtual Image • • can’t detect on paper or screen Sign Conventions • • • object, image, or focal point on reflecting side of mirror has a positive distance Anything behind mirror has negative distance image height is positive if upright, negative if inverted (relative to object) General Physics 2 Geometric Optics 12 Refraction • index of refraction, n, where c = speed of light in a vacuum and v = speed of light in that medium • • • nair = 1 nglass = 1.5 Snell’s Law General Physics 2 Geometric Optics 13 Indices of Refraction General Physics 2 Geometric Optics 14 Total Internal Reflection • • Incident angle where refracted angle (θ2) is 90 is the critical angle at incident angles greater than critical angle, light is totally internally reflected important for fiber optic technology (endoscope) General Physics 2 Geometric Optics 15 Think-Pair-Share • What is the focal length of a plane mirror? What is the magnification of a plane mirror? General Physics 2 Geometric Optics 16 Lens Activity • Use the equipment provided to make an image of the light source on the screen. General Physics 2 Geometric Optics 17 Thin Lenses General Physics 2 Geometric Optics 18 Focal Length, Focal Plane and Power • • f = focal length Power • • • • inverse of focal length P = 1/f measured in diopter (D) 1 D = 1 m-1 General Physics 2 Geometric Optics 19 Ray Tracing General Physics 2 Geometric Optics 20 Thin Lens Equation Magnification Thin Lens Equation General Physics 2 Geometric Optics 21 Sign Conventions • focal length • • • object distance • • • positive if the object is on the side of the lens from which the light is coming (this is usually the case) otherwise, it is negative (virtual object). image distance • • • positive for converging lenses negative for diverging lenses positive if the image is on the opposite side of lens from where light is coming positive for real images, negative for virtual images image height • • positive if image is upright relative to object, negative for inverted images h0 is always positive General Physics 2 Geometric Optics 22 Lens Activity • Find two different object-image distances that create a real image. Describe any differences in the image properties. General Physics 2 Geometric Optics 23 Think-Pair-Share • Sunlight is observed to focus at a point 18.5 cm behind a lens. (a) What kind of lens is it? (b) What is its power in diopters? General Physics 2 Geometric Optics 24 Fermat’s Principle • When light travels between 2 points, its path is the one that requires the smallest time interval. General Physics 2 Geometric Optics 25 Combination of Lenses • When adding two or more lenses in series, the focal length of the combined lenses, f, is: General Physics 2 Geometric Optics 26 Combining Lenses • Measure the focal length of the two double-convex lenses individually. Combine the lenses together and measure the combined focal length. Calculate the combined focal length using the equation. • Calculate the percent error of your measured value. • • General Physics 2 Geometric Optics 27