Fat is made up of a jumble of molecules. The molecules, or chains of smaller atoms, are all squiggly and don’t allow light to pass through them. This is what makes the fat look white.
When you add heat, the molecules in the fat eventually straighten out enough to let light pass through it. This makes the fat clear.
As others said, the fat becomes translucent when melted, explaining why bacon does so as well when heated.
The second observation is more complex, but one possible (in the sense of: it definitely does that; but your instance may have further complications, hard to say without lots of data from your side) reason is as follows:
Many surfaces appear “white” despite the material actually being translucent or reflective. You get that for example with finely sanded glass, snow, and even white clothes. What all those also have in common is that they become translucent or even transparent when wet. But why?
A smooth sheet of glass or a block of ice reflect and refract all light the same, the image is preserved and light passes through mostly unhindered. There is however some small effect everytime the light changes from material to air or back.
Now when there are lots of surfaces to hit or get through, be it millions of icy needles on snowflakes or thousands of fibres, the light gets changed much more and sent all over, chaotically. At low rates the image is distorted and washed out (“translucent”), and at higher amounts most light doesn’t make it through at all and is sent back (“white”).
Adding a transparent liquid such as water or melted fat fills the gaps. Now there are less changes between air and material: white becomes translucent, translucent becomes transparent. When you poke the bacon, some fat escapes, removing this effect again, hence white.
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