Can the Sun be used as a gravitational lens to achieve better telescopic viewing? Can this effect be practically used to view celestial objects?
Yes, it would be possible. There are two roads here:
In case of detecting light in the range of visible wavelength, perhaps you would consider that rare occasion when there is a
solar eclipse. And it may also be possible at times of
Invisible light (outside visible range, beyond the IR and the UV)
Now, other than that, we have telescopes for radio, infra-red, UV rays and X-rays which wouldn't require us to look into the 'eyepiece'. Astronomers have detectors for that and light received is stored in 'pixels'.
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As pointed out by Jeremy in a comment below and also pointed out here, it is actually a far fetched idea. You need to be really far away from the sun to use it as a G-lens. The telescope has to be around 50 billion miles away and to cover that distance within one generation, probably we haven't achieved that technologically advanced level yet.
Actually, one of the first confirmation of GR, is by Sir A. Eddington et al., who measured the deviation of light trays of an unsaid-as-far-as-i-know stars, on May 29, 1919.
Here is an original snapshot from their experiment: They took advantage of a solar eclipse to measure the light bending from the expected position of the sources. The experiment has been a bit contested, but successive experiments of the same type (measures of light bending of Galactic stars during solar eclipses) confirmed those results. And, he was Eddington in the end!
Yes, it is possible to use the sun as a gravitational lens and to achieve better telescopic viewing. As you know space is curved by mass and so light is deflected by mass, it is possible to focus light using gravitational lenses and thus achieving greater telescopic viewing.
However, the sun does have corona fluctuations around it. So, to better exploit the gravitational lensing effect of the Sun, one should try to focus a little bit further away from the sun.
Actually, it was already being planned for a space mission to exploit the sun's gravitational lensing effect to communicate interstellarly. The mission is called FOCAL (For "Fast Outgoing Cyclopean Astronomical Lens").
For more further information, search for either "Dr.Claudio Maccone" or "FOCAL Space Mission"
In a word, no. The light path for a gravitational lens around the sun would be too close to the surface to see the star behind the sun. Usually, a gravitational lens is from a galaxy far away so that the light can converge after passing the galaxy.
Aside from the sun, do you see any stars during the day?