Why does light refract twice in a silvered lens before hitting the mirror?

[dhtikna]

When dealing with lenses which have one curved/flat surface silvered why do we consider light to refract twice before hitting the silver side? This diagram should show what i mean:

The way it appears to me is that after light enters the un-silvered surface it refracts then it does not refract but directly hits the silver surface and reflects. In this case we need to use the following formula:

μ₂/v - μ₁/u = μ₂-μ₁/R

at the two refractions, instead of the lens formula. What's wrong in my thinking?

P.S. This is my first post, sorry that i didn't use the template, i don't see how i can format my question like that

 

[dauto]

The light must come back through the lenses after reflection, refracting a second time. You formula is not very helpful since you did not explain the meaning of the symbols. I can't tell whether it's correct or not. what's μ1? What's μ2? What's v? What's u? What's R?

 

[dhtikna]

sorry,
μ = refractive index on medium
u = object distance
v = image distance
r = radius of curvature of spherical surface

Let me rephrase my question:

For a lens:
Refraction at first surface follow by refraction on second surface;
For a silver lens:
What i have been taught:
Refraction at first surface,again refraction at the second surface(which has been painted with silver),reflection at the second surface,refraction at second surface and finally refraction at first surface

But it look like to me that at the second surface ONLY reflection should take place no refraction

P.S. Can't you edit the original post?