How Does Angular Radius Relate to Deflection Angle in Redshift Calculations?

[stuartgriffin]

Homework Statement

A galaxy cluster of mass 3.0 × 1013M⊙ with known distance of 20 Mpc is observed in the centre of a bright ring, which is presumably a lensed galaxy. The angular radius of the ring from the cluster is 1.13 arcmin. The ring is observed to have a redshift of 0.0075. Assuming a value of 70kms−1Mpc−1 for the Hubble constant, determine whether the ring’s redshift distance is consistent at an accuracy of ~5% to the distance expected for the lensed galaxy to actually be located directly behind the cluster.

Relevant Equations

a=4GM/bc^2
V=H0D

I have attempted to link the equations, but I don't really understand how the data given fits. Does the angular radius get plugged in as the deflection angle?

 

[Orodruin]

What is the distance to the lensed galaxy? How can this help you get the deflection angle?

 

[stuartgriffin]

What is the distance to the lensed galaxy? How can this help you get the deflection angle?

Ahhh, thank you, so I calculate the distance using the redshift and hubbles constant? Am I on the right lines with the equations I am using?

 

[stuartgriffin]

What is the distance to the lensed galaxy? How can this help you get the deflection angle?

Does this look like I'm headed on the right track?