Summary

After having studied this lecture, you should be able to

• derive the Newtonian lensing equation (12.2)
• explain why alignment produces an Einstein ring, and derive its radius.
• explain how micro-lensing works and has been used to search for massive compact halo objects in the Milky Way halo
• explain how gravitational lensing has been used to estimate the mass of galaxy clusters, and hence infer that they contain dark matter.