Conditions for Naked eye visibility of Venus in Transit

The first point to notice is that this is a bright filed observation Ii.e. the object to be detected is dark in an overwhelmingly bright background. There are two aspects of the functioning of a human eye that are of importance in examining this problem.
1. The smallest angle or limit angle that a dark object must subtend at the eye so that can be detected by it.
2. The correct range in contrast between the object and the background that will enable the eye to detect the object. If the background is such the object merges with it, the eye can no longer see it. This is what happens in a dark field observation of stars in a night sky. The light pollution in the cities makes faint stars invisible and you are only able to see the brighter ones.
The usually accepted limiting angular dimension of an object detected by the eye in a bright field observation (called Visual acuity) is about one arc minute at about 2000 lux of luminance(1 lux = 1.46 milliwatts/ meter squared). This angle decreases with decrease in luminance, up to about 0.25 minute of arc at a luminance 100 lux. Lower light levels do not decrease this angle any further.
The angular size of Venus on the day of the transit is 57.8 arc seconds, just a few arc seconds smaller than 1 arc minute. The angular size varies slightly about this value, from transit to transit, depending the distance between Venus and the earth. The luminance of direct sunlight is over a million lux! So, for the high luminance associated with the direct sun light, Venus would be simply swamped by the glare. In fact the sun is such a bright object, that NOBODY is able to or SHOULD actually see the solar disc at all! A person may be able to see Venus as a tiny black dot on the solar disc, if and only if, the glare from the sun is cut down SAFELY. Fully tested and approved filters manufactured for SAFE viewing allow only 1 part in 100,000 of the incident sunlight in the ultraviolet, visible and infra red regions. While these filters will cut out sunlight to about 10 lux, the already black Venus just gets only a little bit darker! So the contrast is still adequate and such filters can indeed help the public to view the transit of Venus safely.