Hard Optics Problem: Calculate Magnification & Image Distance

[reb30]

1. An object (height o) is placed at an object distance S in front of a converging lens. The lens is placed at a distance d<Si (image distance) in front of a very thick glass plate (index of refraction n, thickness larger than image distance). The surface of the glass plate is perpendicular to the optical axis. Calculate the magnification m and the image distance Si



2. Lens makers equation? I'm not really sure



3. I know the magnification will be the same whether the glass is there or not, but I can't actually get any equations out for it :(

 

[chaoseverlasting]

You can find out where the first image will be formed using the lens formula.

That image acts as a virtual object for the glass slab. Here you can use the lens makers formula to find out where the image will be after the first refraction off the glass surface.

Then you subtract/add the thickness of the glass slab to the second image and that's your second virtual object for refraction at the second surface of the glass slab.

There's something else here too, the fact that the glass slab is thicker than the image distance... keep that in mind when you solve it. That'll put a mathematical constraint on your answer somewhere after the first refraction at the slab surface.

 

[reb30]

Thanks for your reply. I had a look at this, but don't understand how you can use the first image as a virtual object for the slab of glass, because it will be inside it. Also, we aren't told the thickness of the glass slab, I think because it is infinitely thick so it doesn't matter.

Any ideas?