How deep to cut engraved images (V-carve or Otherwise)?

Out of curiosity, how deep should someone set depth of cut who either cutting something in a mask or through stain/paint should you cut. Below is a sample project of what I am thinking about.

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Depends how deep you want the cut…I generally use a minimum of about .03"

Thanks for the replies. This was really helpful.

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Phil, what 90 degree bit do you use?