1. Gravitational lensing. You observe a double Einstein ring around galaxy Lambda.
One of the lensed galaxies, Mu, produces an Einstein ring of radius $\theta_m = 7.0''$ and is
at redshift $z_m = 0.15$, while the other lensed galaxy, Nu, produces an Einstein ring of
radius $\theta_n = 9.3''$ and is at redshift $z_n = 0.30$. Assume that galaxy Mu is low-mass and
does not also visibly lens galaxy Nu -- that is, all lensing is due to galaxy Lambda.
Assume $H_0 = 70$ km/s/Mpc.
(a) What is the distance to Galaxy Mu?
(b) What is the distance to Galaxy Nu?
(c) Find the distance to galaxy Lambda in Mpc, and then the mass of galaxy Lambda
in $M_\odot$. (Hint: You'll need a separate lens equation for each Einstein ring, and if
you rearrange them suitably, you can divide them to eliminate the mass.)