Cube Beam Splitter Ratios in Reverse Good day to all,
I the following diagram is a non-polarized beam splitter cube with a 10:90 (R:T) split ratio. The questions I have are:


*

*that when light comes back does the 90°, R path still have a 10% portion and the T path have 90%?

*Would a plate beam splitter of the same ratios behave the same way?

Many thanks in advance...
 A: The following assumes that the beamsplitter cube or plate is made of isotropic material like glass, and that the refractive index of both halves of the cube is the same.  Birefringence and polarization can complicate the story.
So: imagine removing the arrows that are inside the beamsplitter (they just confuse the picture) but leave the arrows on the transmitted and reflected beams.
Now imagine flipping the diagram on the left first on a vertical axis, then on a horizontal axis.  
That flipping process does not change anything about the physics of the situation, but it makes the flipped diagram identical to the diagram on the right.  Now you can easily see the % of light transmitted and reflected.
A plate beamsplitter (one face antireflection coated, the other face thinly aluminized) will work essentially the same way: the transmitted-to-reflected beam ratio will be the same regardless of whether the beamsplitter is used in the forward or backward mode.  
A: I am upvoting the answer by S. McGrew because I think it is correct, at least for simple beamsplitters. Since S. McGrew commented that “the best way to get an answer is to do the experiment”, I just spent about an hour total doing the experiment with a simple beamsplitter cube.
This photo shows a green laser pointer, a beamsplitter cube and two UDT UV100 photodiodes:

The beamsplitter is 50:50, give or take, and note the cage rods on the cage cube: the two photodiodes are in cage plates on the 2 inch rods at right and top.
The next photo shows the output currents of the two photodiodes when the laser pointer is on. Room lights were on, no light baffles were used, etc. Quick and dirty setup: about 30 minutes to do.

Perhaps a little more light transmitted than reflected, but there was a light at the left that may have contributed: the photodiodes are fairly sensitive. I consider these about the same.
Now the third photo shows what happens when the beamsplitter cube is used in reverse. Note the photodetector cage plates are now on the half inch long cage rods.

This is about the same as in the forward direction. Obviously, one quick and dirty experiment cannot be definitive. But for this particular beamsplitter cube, it appears to work equally well, more or less, forward or backward. This makes sense: there is no indication on the beamsplitter cube of a canonical entrance face.
