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Unformatted text preview: Physics 3002, Problem Set 10, due 4/22/09 Lam Hui
1. Ryden problem 8.3. Express your results in arcseconds. 2. In class, we derived an expression for the magniﬁcation of the two images of a point mass lens using: M= θI dθI θS dθS (1) Complete the derivation to show that the magniﬁcation of the two images are: 1 M+ = + 2
1 2 1 2 + 2 θE 2 θS (2)
S 1 + 4 θE 2
2 θE 2 θS 2 θE 2 θS θ2 + M− = − 1+4 1 2 Show that the above expression for M− is correct in the sense that it is always non-negative. Show also that M− + M+ ≥ 1 always - this is known as the magniﬁcation theorem, and can be proven for any gravitational lens, that the sum of magniﬁcation of images always exceeds one. ...
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This note was uploaded on 02/23/2010 for the course PHYS 3002 taught by Professor Lam during the Spring '10 term at Columbia.
- Spring '10