Some Answers to Activities on the Simulations First Draft

In the refraction simulation, the image of a vertical object is vertical for the rays leaving near the normal, but...

The image position rotates(!) and the image starts vertical and becomes nearly horizontal
The image deteriorates, that is the rays don't appear to come back to the same position
Our eyes focus on only a narrow bundle of rays, so we get an approximately focused view of an object (try narrowing the angle of the bundle of rays and you'll see what I mean)

For the critical angle, the emerging rays travel right along the surface, so theta = 90 degrees. For a lower index of 1.5 and an upper index of 1, 1.5 sin theta(critical) = 1 sin (90 degrees), and theta(critical) is arcsin(2/3) = 42 degrees. You should have found about this answer as you played with the simulation (I got about 41.4 on the simulation, which is close).

In the mirror simulation you can push the mirror or pull it when the object 'locks on' to the mirror. I have found that by first making the object as tall as the mirror, letting go of the head, then clicking near the axis about 10 units away from the mirror vertex (about 1 red division) I can get the object and mirror to separate.
For real objects in a mirror concave toward the object, we get real images for all object distances greater than the focal length. (The object is farther away than the focal point from the mirror. The image distance, object distance and focal length are all positive.) Closer in, we get virtual images, where the image distance is negative.
For real objects in a mirror convex toward the object, we get real images nowhere and virtual images everywhere. No matter where we put a real object, we get a virtual image.