How to stop spectacle from slipping?
spectacle anti-slip mechanics
The nose pad provides the most effective support when the user is looking straight or slightly down.

rubberized nose-pad
Rubberized nose-pad for greater friction to reduce spectacle slipping
When straight ahead or down slightly, the friction from the nose pad and the spectacle temple prevents the spectacle from slipping down. In metal frames, the nose pad may be adjusted such that its surface makes maximum contact with the nose bridge. This will reduce the pressure on the nose bridge and maximize the friction coefficient between the contact surface. For plastic spectacles, the nose pad may be smooth and not easily adjustable. Any pressure point may cause increased accumulation of facial oil or perspiration which cause it to slide. Replacing the nose pad with or sticking a rubber/silicone nose pad onto existing nose pad will provide additional friction to keep the spectacles in place. Alternatively, there are coatings that can be applied to the nose pad that increases the friction [See http://www.nerdwax.com/].

Increase friction at the spectacle temple/arms or adjust the bend to prevent slipping.
When you tilt your head down until it is pointing downwards, the friction from the nose pad diminishes until zero. The friction exerted by the pressure of the temple on the head remains and the bend on the temple/arm supported by the ear is needed to prevent the spectacle from dropping off. However, as the bend was adjusted to be slightly loose so that there is no discomfort at the top or back of the ear, there will be noticeable slipping of the spectacle. To stop the slipping, one way is to use rubbery temple sleeves to increase the friction between the contact surface of spectacle temple and your skin. The difficulty of this is that it is not easy to find a suitable temple sleeve that could fit over and even if it fits, pulling the sleeve over the temple will take some patience. The use of shrink tube has been suggested and has been reported to be good enough to prevent spectacle slipping. Although easier to put over the temple, it requires the right amount of heat (typically from a heat gun) to shrink the tube over the temple. The added thickness to the temple will increase pressure on your head and this may sometimes cause discomfort.
Temple hook is easily adjustable and can provide sufficient anchorage to prevent slipping while gentle to the top and back of the ear.

Spectacle hook
Image courtesy of Beta-Simplicity

Simple fix like having elastic bands or tubing over the temple has been reported to be good enough to stop spectacle from slipping. However, if the spectacle lens is heavier, such simple fixes may not be adequate. Further support at the spectacle temple may come in the form of hook or stopper that slides over the temple and poistioned such that it just touches the ears from behind. This stops the spectacle from slipping using friction and as physical anchorage. These are normally made of soft materials so that they are comfortable at the point of contact. There are different designs and materials and their comfort level varies. These temple hooks are very effective in preventing spectacles slipping and they can be adjusted along the length of the spectacle temples until the right level of fit is achieved.
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