Exercises 3 for RÖ3 (2 March)

1. A grating with 600 grooves/mm is illuminated by collimated light at an angle of 10^o from the normal. What is the angular dispersion at a wavelength 500nm in the m=+2 order?
   
   
2. Two stars were observed with a photometer on the Danish 1.5 m telescope at ESO. One of them was a standard star, E4-h with known magnitudes:
   U=14.461, B=14.375,V=13.760, R=13.376, I=12.993
   Now you want to compute the corresponding UBV magnitudes for the second star, star 3.
   The observed sky subtracted countrates for the two stars were:
   for E4-h (observed at airmass=1.046)
   U=224.0 counts/sec, B=2120.6 counts/sec,  V=5352.3 counts/sec
   for star 3 (observed at airmass=1.534)
   U=44.5 counts/sec, B=538 counts/sec, V=1560 counts/sec
   
   Typical extinction values for the ESO observatory at La Silla are given in the ESO users manual as:
   U=0.44 mag/airmass
   B=0.19 mag/airmass
   V=0.12 mag/airmass
   
   
3. The Arecibo radio telescope in Puerto Rico is a 305m diameter filled-aperture spherical dish, while the Very Large Array in Socorro, New Mexico, has nine 25m diameter parabolic dishes on each of the three arms (27 dishes in total), radiating out at equal 120 degree angles to one another; each arm is 21km long. Calculate the ratios of (a) the total collecting areas, (b) the angular resolutions, of the two telescopes. Give an example of  an observation for which c) Arecibo is better than VLA and d) VLA is better than Arecibo.