# Homework Help: Gravitational Lensing and Angular Diameter Distances

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1. Nov 17, 2016

### maxhersch

1. The problem statement, all variables and given/known data

Given this diagram, the problem is to find an expression for β/ΘE in terms of X/ΘE and Y/ΘE.

2. Relevant equations
β = Θ – α(Θ)
Dsβ = DsΘ – Dlsα'(Θ)

3. The attempt at a solution
I really only need help starting this problem. In my textbook and every document I can find online about gravitational lensing it says that the distance from the lens to the source is not simply the difference between the distance from the source to the observer and the distance from the lens to the observer. They say that this is because these distances are actually angular diameter distances and that we will learn about them later on.

What I would like to know is if you are given the distance to the source and the distance to the lens, how do you get the distance between the source and lens? The textbook seems to tell you how not to calculate it, but then they don't explain how to calculate it until 5 chapters later. Meanwhile in my homework I have this problem along with another problems that asks me to use distance to source and lens to find the Einstein radius of the lens, which also requires a value for β. Maybe I am missing something obvious but any help would really be appreciated.

2. Nov 22, 2016