As always, answers should include the necessary work and discussion 
so that they would be understandable to a typical literate reader.

1) Could a Porro prism be constructed with water as its transparent 
medium to be used as a retro reflector which would send a beam 
back in the direction from which it came?  How about fused quartz?

2) The primary mirror of the 18 inch (.46m) scope is f/3.  What 
is its radius of curvature?

3) You have the following data:
- pointed at a star on the celestial equator and nearly due 
east you find the star drifting north in the eyepiece about 
3.5 arcminutes in 5 minutes of time
- pointed at a star on the celestial equator and nearly due 
south you find the star drifting north in the eyepiece about 
1.5 arcminutes in 5 minutes of time
What do these data tell you about the alignment of the polar axis?

4) The GTC will have a focal length of 17000 cm at the Nasmyth 
focus.  What is the expected inverse image scale in arcseconds per mm?

5) Write the equation for the Raleigh resolution criterion 
(in arc seconds) for a telescope to be used at 1.2 micrometers 
wavelength (in the IR) when the aperture is used in meters.