Insect and Spider Identification: CLOSED: What is this white stuff on my Rosemary?, 1 by PeterGrimes

PeterGrimes wrote:
Hi all,

Here are a couple of pics of something that's covering about 1/3 of the upper leaves of our rosemary plant. This is an indoor plant, but we got it from the farmer's market. I'm afraid to go near the plant, as any disturbance results in a veritable fog of this dust - and I don't want it infecting my other plants!

What is it, and what are some eradication techniques?

Any help is much appreciated :)