Assume there is a very thick glass (e.g. 3cm) in front of the mirror.
An object is allocated away from the glass (distance =10cm, object to glass=10+3=13cm)
The question is: where is the image of the object (distance from mirror=? cm)
The following let you play with the simulation to find out the answer.
The initial condition is the same as above.
You can change the location of the object with mouse drag and drop,
or change index of refraction/thickness of the glass with sliders.
Click play to start the ray tracing.