The Sun as a gravitational lens Since the Sun is a gravitational lens with as focal length of 550 AU for visible light, with an immense amplification factor, shouldn't it light up objects hanging out there?
We should get solar sails up there to finally boost them somewhere interesting, opposite to the star that is emitting the light.
For neutrinos, I've heard that the focal length is 110 AU. Wouldn't a massive neutrino bombardement trigger interesting nuclear reactions (maybe that's not an astronomy question)?
 A: A lens will focus light, and the sun's gravity does indeed focus light from objects behind it. The issue is that all stars aside from the sun are very far away so even with focusing, you will still not get anything like the equivalent of the sun's output. And there won't be massive bombardment of anything - despite having a focus, there just aren't enough particles available to be focused.
Also, that focal length. 110 AU - that's a very long way out. Pluto is about 40 AU out. Voyager 1 is about the right distance - it has been travelling for over 30 years.
And finally, at that distance out - a spacecraft may be at the focal point for light from a star, but the sun moves, the spacecraft moves...focused light from that star isn't going to be at that point for long.
A: Individual objects can act as gravitational lenses, this is referred to as microlensing. If you watch a group of stars for long enough, some will get brighter for a short period of time.
Gravitational lensing is more closely associated with much more massive objects such as galaxies and galaxy clusters.  The Sun is simply too small to do much to light passing by other than give it a slight deflection, here's Wikipedia's take on it, light deflection by the Sun.
A: There will not be any kind of "massive bombardment" and it won't "light up" things out there.
However, using the Sun as a gravitational lens for a radio telescope is a real possibility.  There was a lecture at the SETI Institute on 11/25/2009 titled "Deep Space Flight and Communications: SETI, KLT and Astronautics in a 2009 book" by Claudio Maccone, Co-Vice Chair of the SETI Permanent Study Group, International Academy of Astronautics.  Here is a link to the page where you can download a .zip file of the presentation and you can see the video of the talk here.
The problem is that you have to choose exactly the one target that you want to image and then launch a space craft with, say, a radio telescope out to between 550 and 1000 AU on exactly the other side of the Sun from that object.  For example, you might use this to image the black hole at the center of our galaxy, or if you got a SETI signal from a star you might deploy a satellite to examine it closely.
The reason it won't light up objects is because the gravitational field of the sun does not act like a perfect lens. In particular, at the distance of 550 AU only radio waves that just miss the limb of the sun will focussed to that point. At a greater distance, say 700 AU, there will be a ring further away from the sun where all rays will be focussed.  The width of the ring that is focussed depends on the size of the radio dish on the satellite. The big advantage for signal gathering capabilities is that it is like having many many dishes of that size forming a ring around the sun!
UPDATE: For any of you in the south San Francisco Bay Area, there is a special colloquim at SLAC tomorrow (Friday, Dec 2, 2011 at 11AM).  See the announcement and details here.
A: How does 200 metre resolution at Alpha Centauri grab you?
http://www.cesr.fr/~pvb/gamma_wave_2005/presentations/optics/Koechlin.pdf 


*

*Wherever in space there are intelligent creatures like us, they
will be driven to explore and understand our universe, just as we
do. We and they wish to see to the farthest depths of space with
the greatest clarity allowed by the laws of nature. To this end, we
build, at great expense, ever more powerful telescopes of all
kinds on Earth, and now in space.

*As each civilization becomes more knowledgeable, they will
recognize, as we now have recognized, that each civilization has
been given a single great gift: a lens of such power that no
reasonable technology could ever duplicate or surpass its power.
This lens is the civilization's star. In our case, our Sun.

*The gravity of each such star acts to bend space and thus the
paths of any wave or particle, in the end creating an image just as
familiar lenses do.

*This lens can produce images which would take perhaps
thousands of conventional telescopes to produce. It can
produce images of the finest detail of distant stars and
galaxies.

*Every civilization will discover this eventually, and surely
will make the exploitation of such a lens a very high priority
enterprise.

*One wonders how many such lenses are being used at this
moment in time to scan the universe, capturing a flood of
information about both the physical and biological realities
of our time.
6

*Frank Drake, 1999, from his Foreward to Claudio’s book.        

