I’m bringing this question back, someone posted it 9 years ago and there was one comment that has since been deleted. I need to know so bad. I can’t find the answer ANYWHERE.
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Your breath is warm and full of water vapor from your lungs. If it cools down, it will be itching to deposit that water on any nearby surface.
The glass is (usually) a lot less warm than your lungs, so the water precipitates out onto the surface of the glass as a liquid.
If you blow faster air from farther away, the air from your lungs has more time to mix with its surrounding air. On one hand, this cools it down and so it will be trying to offload some water, but on the other hand there is lots more air to help carry the water. Whether the water is fully caught by the surrounding air or deposited onto glass depends on the temperature, humidity, and airflow.
Glass fogs up when it cools down warm moist air below the dew point, which makes some of the moisture in the air settle on the glass. When you exhale slowly, the glass gets lots of time to cool it down. When you blow harshly, the air never gets cooled down much, and you also entrain fresh, drier air which can carry away vapor from any water that is on the glass.
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