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Unformatted text preview: PHYS 434: Assignment 3 solutions Problems 4.3 Use the paraxial approximation (Equation 5.8). Proceed as in Example 4.1: sin sin = e where e is the error, in this case e = 0.001 . Thus = 1 + e ( ) sin Trial and error will suffice, but it is better to use a Taylor series: 1 + e ( ) 3 3! Thus = 3! 1 1 1 + e 6 e = 0.775 rad Use the small angle approximation again, this time with the tangent: tan = D 2 f D 2 f = 7.75 mm The above approximations yield 3-digit accuracy more than sufficient for a 1% tolerance window. Problem 4.4 Ray diagrams for problem 4.4. (a) s o = 2.75 f . (b) s o = 0.750 f . Proceed as in example 4.2. Let s o = 2.75 f . The image distance is s i = f s o s o f = 2.75 f 2 1.75 f = 1.57 f The image distance is positive, so the image is real. The magnification is M = s i s o = 0.571 M < so the image is inverted, with a height of 0.571 cm. See ray diagram figure. so the image is inverted, with a height of 0....
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This note was uploaded on 04/11/2010 for the course PHYS 434 taught by Professor Kilfoil during the Winter '09 term at McGill.
- Winter '09