solutions-ps10

# solutions-ps10 - Physics 341 Problem Set#10 solutions 1 In...

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Physics 341: Problem Set #10 solutions 1. In this problem you will calculate a microlensing light curve. In the ﬁgure below, the dashed straight line represents the trajectory of a point source passing behind a point mass lens (the solid dot in the center). The circle indicates the Einstein radius. The x and y axes show the angular distance from the lens, measured in units of the Einstein radius: x/θ E and y/θ E . We will assume that the motion is in the x direction, so that y is constant and equal to the impact parameter . The ﬁgure shows the case of an impact parameter y = 0 . 5 θ E , but we will consider a range of values. x/ θ E y/ θ E β / + ! (a) Use the Pythagorean theorem to write down an expression for β/θ E (the angular separation between the source and lens), in terms of x/θ E and y/θ E . As shown in the ﬁgure above, the angular distance from the lens to the source, β , is just given by the Pythagorean theorem: β θ E = s ± x θ E ² 2 + ± y θ E ² 2 1

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(b) In class we showed that this conﬁguration produces two images, on opposite sides of the lens. The images, source, and lens all lie along the same line. The angular separation between the lens and each image ( θ + and θ - ) is given by: θ ± = 1 2 ± β ± q β 2 + 4 θ 2 E ² = θ ± θ E = 1 2 ³ β θ E ´ ± s ³ β θ E ´ 2 + 4 The magniﬁcation of each image μ and the total magniﬁcation μ total are given by μ ± = θ 4 ± θ 4 ± - θ 4 E = ( θ ± E ) 4 ( θ ± E ) 4 - 1 μ total = | μ + | + | μ - | (Negative magniﬁcations correspond to ﬂipped images, so the total magniﬁcation is the sum of the absolute values.) With these equations you are ready to proceed.
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## This note was uploaded on 10/18/2011 for the course PHYSICS 341 taught by Professor Keeton during the Fall '08 term at Rutgers.

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solutions-ps10 - Physics 341 Problem Set#10 solutions 1 In...

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