The next generation of ground based telescopes will have pri- mary mirrors tens of meters wide. the thirty meter telescope (tmt), with a primary site choice of manua kea, is an example of such a telescope. (a) how much more light will tmt collect compared to the keck 10-m tele- scope currently in operation? (b) the tmt will have a naysmyth focus with a total focal length of 450-m. what is its plate scale (in arcseconds/mm)? (c) imagine that a particular instrument employs a 2048 x 2048 ccd detector that is 2.66 cm across (this is similar to a camera called megacam on the cfht). what is the field of view of the camera in arcseconds? can it fit jupiter? what about neptune? (feel free to looks these up! ) (d) your professor studies weather patterns on unresolved brown dwarfs (r~rjupiter) by obtaining light curves that measure how a brown dwarf's brightness changes as it rotates and cloud features come in and out of view. will tmt finally be able to resolve surface features on the nearest brown dwarf (at a distance of -6.5ly)?