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Solution3

# Solution3 - PHYS 434 Assignment 3 solutions Problems 4.3...

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PHYS 434: Assignment 3 solutions Problems 4.3 Use the paraxial approximation (Equation 5.8). Proceed as in Example 4.1: θ sin θ sin θ = e where e is the error, in this case e = 0.001 . Thus θ = 1 + e ( ) sin θ Trial and error will suffice, but it is better to use a Taylor series: θ 1 + e ( ) θ θ 3 3! Thus θ = 3! 1 1 1 + e 6 e = 0.775 rad Use the small angle approximation again, this time with the tangent: tan θ = D 2 f θ D 2 f θ = 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 .

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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 < 0 so the image is inverted, with a height of 0.571 cm. See ray diagram figure. Let s o = 0.75 f . The image distance is s i = 3.00 f . s i < 0 so the image is virtual.
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