Magnitude and Angular Scales

These images are recorded with a 16 inch diameter telescope operating at $f/10$, that is, with a focal length $10\times$ the diameter. The focal length of this telescope is therefore about 160 inches or 4064 mm. The pixels are separated by 9 microns center-to-center on the detector.

1. A displacement from the center of the image by a distance $r$ corresponds to an angle $\theta$ such that $r=f\tan\theta$. What is the image angular scale in arc seconds per pixel, and the total field of view (width by height)? There are 1530x1020 pixels on this device.

2. Use the image m1_600s_01d.fits with ds9. Adjust the
   Scale->Parameters to get the best rendition of this supernova remnant nebula and its faint stars. Set the Zoom->Invert Y so that north is at the top of the displayed image. Use xephem's View->SkyView and find the Messier object M1 in Taurus. Zoom in to the map of the M1 region until the field of view is about 0.2 degrees. Identify a few stars in this field, and try to measure the angular scale of the image by using the coordinates for stars you can identify. How close is this angular scale to your calculation? Can you explain the differences?
3. What is the faintest star you can identify in this image?