Q:

Looking through a glass hemisphere

I've found the following question on IsaacPhysics.org . I've been working on it for a couple of hours but I cannot figure it out.

A looking glass is used to read an ancient scroll. This lens has a hemispherical shape with radius R and its flat surface is placed on top of the scroll being examined. The lens is made of glass of refractive index n. The reader is a distance h from the scroll along the axis of symmetry.
What is the minimum value of h for which the entire circular area of the scroll directly under the lens is visible to the observer if $R=3.70\ \rm cm$ and $n=1.30$?

A:

I have tried to workout at what angle there would be total internal
  reflection. My reasoning was that at a greater angle than that no
  light would pass and thus the scroll not entirely visible.

I think your direction is correct. Here is a diagram that might help you figure that out.

Red lines represents the light path from points A and B of the scroll to the observer at point E.
If point E is moved down, you may find that, for the Snell's law to hold for the BDE light path, point D would have to move down the circle and line DE would become closer to the tangential line, which would indicate that we are approaching the point of the total internal reflection.

