Is it safe to observe the sun through binoculars with welding glass in front? I asked this on Reddit but didn't get much of a response.  So here goes!
I'm looking for low-cost ways to observe the Transit of Venus this summer. Since I'll only be able to see a few hours of it from my location, and it very well may be cloudy, I don't want to spend big bucks on solar filters.
I've been reading though that shade 14 welding glass will block enough light. What I want to know is if it's still safe to view the sun through binoculars after light has passed through the welding glass. Here's how I'm thinking the arrangement would look:
Eyes  <-  Binoculars  <-  Shade 14 welding glass  <-  Sunlight

Thanks!
 A: While it looks like Shade 14 glass will block out the light, I would still advise against this because if the glass slips out at any point you could be blinded pretty much instantly.
I always recommend projection viewing - this also has the advantage of being a very social exercise: you can point at features, and discuss what you see.
A: Personally I wouldnt risk it, the chance of mechanical failure is too high, ie the glass falls out of place during viewing...
But according to here, shade 14 glass should be good, but without the equipment to test it, how can you be sure other than testing on your retina...
A: Placing the solar filter before sunlight hits the instrument is the correct way of doing it. You could put the filter after the instrument, provided you don't mind being blind - the concentrated energy from the Sun heats up the filter, which sooner or later melts (if it's plastic) or cracks or explodes (if it's glass), your eye(s) receive a full dose of that energy, say hi to the white cane and the friendly guide dog.
ALWAYS, ALWAYS, ALWAYS use solar filters installed in front of the instrument (telescope, binoculars, etc.). In front of it, ahead of it, on top of it. DO NOT use eyepiece filters when looking at the Sun. Do not make any mistakes here.
HOWEVER, even mounted ahead of the scope, any improvisation with regard to solar filters is bound to come back and bite you in the ass sooner or later. Look at professionally-made solar filters for telescopes, they are specifically fitted to the scope's external diameter, and have various mechanisms to secure them in place, such as triple screws, etc.
http://astrozap.com/scripts/prodList.asp?idCategory=31
The last thing you want is the filter to fall off because you tilt the instrument the wrong way, or because the wind is blowing a little. If focused sunlight hits your eye, you will lose vision! There is zero doubt about it.
Even with professionally-made filters, you need to make sure they are secure in place after you install them. Tug them a little, see if they have a tendency to peel off and fall down. If they do, that's a full stop to whatever you're doing at the moment.
A little math:
Let's say the absolute minimum pupil size for your eyes is 2 mm. That's about 10 mm^2 area.
Let's say you're using 50 mm aperture binoculars. That's nearly 2000 mm^2 area. That's 200x bigger than your pupil.
All the energy collected by the 50 mm aperture, which has an area 200x greater than your pupil, is injected in your eye. It's like looking into the Sun, except 200x worse.
See why you must be absolutely certain that the filter never falls off, cracks, melts, or has any other sort of malfunction?
A: I'm not sure what you consider big bucks, but you can get a 25cm by 25cm sheet of Baader Astrosolar Safety Film for ~$30-40; which combined with a sheet of poster board and tape can be used to make filters for multiple pairs of binoculars or telescopes.
Companies selling the filter material can be easily found via Google, instructions on how to make the filter are provided by the manufacturer.  Especially if you're going to be doing a public viewing; I'd suggest using duck tape to secure the filters to your optics.
A: Yes, it's safe to view through the binocular if the sunlight has gone through the Shade 14 glass first.
However, it could possibly fit poorly or slip, allowing sunlight through.  Even just the thinnest ray of unfiltered sunlight will give you immediate blindness.
It's for you to decide if it's worth the risk, but I personally would not take the risk.  There are many other options, such as using the projection method, or making a good-fitting filter.  You can find some good solar filter material on eBay for $10-20.
Then take a little time to put together a good fitting frame for it, and you're all set!
A: I'll just add that it is easy to DIY a secure filter mount that could not come off the binoculars or telescope accidently and that you should do that even using a commercial filter made for you telescope.  I am adding electrical tape to secure the filter designed for my WO ZS80 and using cardboard, duct tape and welder's glass to make a filter for a camera.
