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IV. Optics Nature of light. Spectrum of electromagnetic waves. Wavelength decreases Frequency increases Note: 1 nanometer = 10-9 meter A. Geometric optics 1. Wave front and rays rays wave fronts normal to surface 2. Reflection in 1 2 1 2 out 1 2 diffuse reflection 3. Refraction: Snell’s Law n1 sin 1 n2 sin 2 index of refraction: n1 v2 2 n2 v1 1 f1 f 2 Example: 1 n1 n c v 1 2 n1 sin 1 n2 sin 2 n3 sin 3 2 2 n2 n3 3 3 is independen t from n2 If n3 n1 3 1 Example: n1 1.00 n2 1.33 1 50 2 ? n1 sin 1 n2 sin 2 n1 1.00 sin 2 sin 1 sin 50 n2 1.33 2 35 Example: Equilateral triangle n1 n4 1.00 n2 n3 n 1.52 1 45 4 ? n=1.52 n1 sin 1 n2 sin 2 2 3 60 n3 sin 3 n4 sin 4 2 27.7 3 32.3 4 54.3 sin 1 n sin 2 2 3 60 n sin 3 sin 4 sin 1 sin 2 n 3 60 2 sin 4 n sin 3 4. Total internal reflection n1 1 n2 n1 2 n2 2 n1 n2 1 0 1 90 0 sin 1 1 0 2 90 0 sin 2 1 n1 n1 0 sin 2 sin 1 1 n2 n2 n2 n2 0 sin 1 sin 1 1 n1 n1 0 2 C 0 1 C n2 sin C n1 Example: n2 1 1 n1 n 1.52 n1 n 1.52 sin C n2 1.00 C 41.1 C ? Example: A ray of light is incident in air on a block of a transparent solid whose index of refraction is n. If n =1.38, what is the largest angle θ1 for which total internal reflection will occur at the vertical face (point A)? 1 1 n 2 90 3 sin 3 2 A sin 1 n sin 2 3 sin 1 n sin 90 3 1 n cos 3 n 1 sin 3 n 1 2 n 2 1 n 2 sin 1 1.382 1 0.95 1 72 n=1.38 Example: 1 sin C n C α α n=1.52 sin 90 α 1 n 1 1 cos n 1.52 49 4a. Applications of total internal reflection 1) Binoculars often use total internal reflection; this gives true 100% reflection, which even the best mirror cannot do. 2) Fiber optics. Light will be transmitted along the fiber even if it is not straight. An image can be formed using multiple small fibers. 5. Plane mirror O do di do I O do = di di I Image: virtual erect the same size This is for plane mirrors 6. Comments about objects and images created by different optical instruments (curved mirrors, lenses and their combinations) Image: real or virtual erect or inverted lager, smaller, or the same size as the object