I can try to work through the math later, but I viewed the 2012 transit on the east coast of the USA where it ended at sunset. We were using images projected through binoculars or small telescopes onto the side of the building. As sunset approached, you could see the Sun get dimmer, AND see the side closer to the ground be dimmer than the side farther from the ground*. Near the end (like the last minute) the Sun's image was stretched out.
As for projecting the image of the Sun in general, I've done it with binoculars and telescopes. You just focus the scope so that the image projects on your screen, which is a foot or two away. It also helps to use a sunshield to block the direct sunlight, so the screen is only lit by what goes through the telescope. (Also, if at a public event, keep people from looking through the telescope. Especially relevant as there are filters that let you observe the Sun safely, and if people see some telescopes for direct viewing and some for indirect, one has to be clear which is which. This is why we used the wall as a screen -- easier to control the crowds so no one could blind themselves.)
(IIRC, the transit of Venus was just barely visible to the naked eye (with protection) -- we had some solar filters and you could make out a black speck on the Sun)
* In binoculars, this is right side up, but telescopes invert the image.
I'll try to project an image through binoculars on the next sunny day, to see how it works (taking very great care!) If - and only if - you have time to do the calculations for the exit time, that would be brilliant. I can approximate it if necessary from Cape Town and St Helena but it'd be awesome to have the correct times.
"I'll try to project an image through binoculars on the next sunny day, to see how it works (taking very great care!)"
Something to know about that: you don't want to project a little image of the sun, like burning something with a magnifying glass. You want to pull the binoculars farther back from the wall (with one lens covered) so you're projecting a much larger image. The image of Venus in my projection was about the diameter of a BB.
Yay! Wish I'd known all this three years ago. I drove through floods (admittedly just a few inches deep) to get to a big telescope, which isn't inappropriate given what the 18th century astronomers did - but if I'd had the brains to set up my binoculars to see the exit..!
As for projecting the image of the Sun in general, I've done it with binoculars and telescopes. You just focus the scope so that the image projects on your screen, which is a foot or two away. It also helps to use a sunshield to block the direct sunlight, so the screen is only lit by what goes through the telescope. (Also, if at a public event, keep people from looking through the telescope. Especially relevant as there are filters that let you observe the Sun safely, and if people see some telescopes for direct viewing and some for indirect, one has to be clear which is which. This is why we used the wall as a screen -- easier to control the crowds so no one could blind themselves.)
(IIRC, the transit of Venus was just barely visible to the naked eye (with protection) -- we had some solar filters and you could make out a black speck on the Sun)
* In binoculars, this is right side up, but telescopes invert the image.
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Something to know about that: you don't want to project a little image of the sun, like burning something with a magnifying glass. You want to pull the binoculars farther back from the wall (with one lens covered) so you're projecting a much larger image. The image of Venus in my projection was about the diameter of a BB.
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