 Greetings and welcome to the Introduction to Astronomy. In this week's special topic in astronomy, we are going to talk about the gravitational lens and what this means and how it works. So, what is a gravitational lens? Well, this occurs when light is bent by passing something with mass. Now, it will occur with any object that has mass. However, the greater the mass, the more the deviation will be. So, this is a consequence of general relativity, which explains how light is bent as it passes near a large object. Now, why is it bent? Well, because under general relativity, gravity is a deforming of space and time. So, the object here, the white dwarf, is deforming the space around it. Now, light wants to travel in a straight path. But because of the curvature of space and time, instead of traveling straight, it ends up curving around near this massive object to reach us here on Earth. So, when we look out, we see it as coming from this position instead of its actual position over here. Now, this was actually measured in 1919 during a solar eclipse looking at positions of stars behind the eclipsed sun and noting that their positions were different than they were six months before when the sun was not in that area. So, this occurs on larger scales as well. It's not just for individual stars or our sun. We can see this in things like galaxies, and galaxy clusters can also do the lensing. So, here we see a galaxy and in front of it, between us and Earth, there's a cluster of galaxies. So, all of these are other galaxies and they form a total gravitational field so that the light coming from this object here, this more distant galaxy, gets twisted around. It has to follow curved paths through the gravitational field of the galaxy cluster. And this will cause the image to be distorted and to be much brighter than it otherwise would be. So, there can easily be cases where we would not even see this galaxy but we can see the magnified distorted image is that have passed through the gravitational lens. Now, let's look at one more example of this and here we have an actual image taken and we see the galaxy cluster. Now, the galaxy cluster is all of these galaxies that we see here. So, there's an example, there's several down here and then a couple more here. A whole bunch of galaxies and as the light from a distant galaxy passes through them, it gets distorted. So, we end up with this arc instead. Now, that's not a distortion of the actual galaxy itself, it's a distortion of its light. Could we actually see that galaxy behind the cluster? It would look like a normal galaxy. However, when its light passes through, it gets distorted and brightened by the lens, by that gravitational lens of the whole cluster of materials, all the mass of that cluster. Now, how does this help us? Well, this helps us in that we get a better understanding of the mass of these galaxies and galaxy clusters. And it has contributed to our understanding of dark matter. Because we know the amount of mass that is needed to bend, to do the bending that we see, since we can't find that amount of mass in the cluster of galaxies itself, just looking at those galaxies and all of the detectable gas and stars and any other material there, that there has to be some portion of that material, in fact a very large portion, that is what we call dark matter. And this is one of the ways that we can detect that. So, let's finish up with our summary. So, a gravitational lens itself occurs when light is bent when it passes near some object with mass. The greater the mass, the greater the bending. That distant object, the light from it will be distorted, so it will not look like it normally would, and it will be brightened, brighter than it normally would be by the effects of this gravitational lens. And the distortion can be used to infer the mass of the lensing object. Could be a star, could be a galaxy or a galaxy cluster. And this has greatly improved our understanding of the amount of dark matter that exists in the universe. So, that concludes this lecture on gravitational lensing. We'll be back again next week for another special topic in astronomy. So, until then, have a great day, everyone, and I will see you in class.