Mirror: refractive index and thickness

[HappyBlue]

Homework Statement

Hello everyone ! I hope this is the correct place to ask.
Here is my probem: I have to measure the refractive index and the thickness of the glass part of a mirror.

The idea that I have, and that has been approved by my teachers, is the following:
In order to measure the refractive index of the glass part, I have to get to the point of total reflection with a laser. Once the light comes from that angle, I should not see any fringe on a screen that collects the reflected rays. However, I first thought that the disappearance of the fringe will be due to the total reflection of the air-glas interface, which is not possible as the index of the air is lower than the one on the glass. Therefore I thought that the absence of fringe would be due to the total reflection on the glass-air interface (inside the glass part of the mirror), but in that case the angle needed to obtain that inner total reflection is 90° (which means the laser must arrive parallel to te mirror, which is not possible) (I use Snell-Descartes's equtions

Do you have any idea as to how to proceed in order to mesure the refractive index ?

N.B.:This is the part that is blocking me, I already have to equation to measure the thickness of the mirror once I have the index

 

[berkeman]

Welcome to the PF.

In order to measure the refractive index of the glass part, I have to get to the point of total reflection with a laser.

Do you mean total internal reflection (TIR) inside the glass at the glass-air interface? If so, can you use a prism of some kind to couple the laser into the glass at a low angle?

And it seems like there would be simpler ways to do this. Can you derive both the thickness and refractive index with 2 measurements of laser beam offset using 2 different entry angles? Or does that not give you enough information to calculate both the thickness and refractive index?