Conical mirrors

     I have been researching conical mirrors and what I have fond out so far is that it is best to have a slimmer conical mirror gives you a larger viewing radius than a wider version because, if you multiply the reciprocal of the slope of the mirror by arc-cos it will give you the angle of the viewing radius the larger the slope the lager the viewing radius, though you can have the same viewing radius with both by just changing the the focal length because the smaller the focal length, the larger the aperture or viewing radius will be, but if the focal length is the same than the mirror with the largest slope will give you the largest viewing radius. The only thing is that I have not fond out how to find the viewing radius of the 'teardrop' shaped conical mirror because of the concave shape at the top which makes it very hard for me to preform any math on it because of the concave top, to find the other ones you just have to use basic trigonometry but I don't know how to find the viewing radius of a concave mirror I do have the formula for finding the viewing radius but I do not know how to do it (I don't know if I'm just making this overly complex, but the formula is at the bottom ). I also fond an interesting article of people using conical mirrors with robotics (Here is it URL:http://robotti.wikidot.com/mobilerobotquestions).