Sign convention for real and virtual rays in lenses and mirrors

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physics user1
What kind of frame of reference do I have to choose when I'm studiyng lens and mirrors?

As far as I know you consider positive the direction where the rays are real and negative the one where the rays are virtual, is that always true?

Why can't we study a problem of optics choosing a frame of reference as we are supposed to do when we are studiyng a problem of dynamics?

Is there a more formal motivation?

As far as I know is because the equation 1/p + 1/q = 1/f is correct only when we are considering negative the virtual rays and positive the real ones, the same for mirrors.

Just another thing, why is that equation correct also for mirrors? I know the demonstration but is there something Inew the nature that makes this special
 
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