Your question: "You often hear the term 'speed of light' as the fastest. What about speed of sight? how can we see hubbles deep field so soon?"
Your propensity to conflate neural visual processing with the speed of electromagnetic radiation is a mistake.
Further, your phrase, "see hubbles deep field so soon" is completely unwarranted.
If you were serious, you would make some effort to define what that means.
Vision is not related to the speed of light, which is much faster than neurons can process visual stimuli.
"The Neural Basis of Visual Perception"
The Rockefeller University Hospital
Accessed 18 October 2015:
• http://centennial.rucares.org/index.php?page=Neural_Basis_Visual_Perception
"Sensory Systems - MIT OpenCourseWare"
Accessed 18 October 2015:
• http://ocw.mit.edu/courses/brain-and-cognitive-sciences/9-04-sensory-systems-fall-2013/
"The Hubble Deep Field (HDF) is an image of a small region in the constellation Ursa Major, constructed from a series of observations by the Hubble Space Telescope. It covers an area 2.5 arcminutes across, about one 24-millionth of the whole sky, which is equivalent in angular size to a 65 mm tennis ball at a distance of 100 metres. The image was assembled from 342 separate exposures taken with the Space Telescope's Wide Field and Planetary Camera 2 over ten consecutive days between December 18 and December 28, 1995."
• https://en.wikipedia.org/wiki/Hubble_Deep_Field
• https://en.wikipedia.org/wiki/Speed_of_light
"Hubble is one of NASA's most successful and long-lasting science missions. It has beamed hundreds of thousands of images back to Earth, shedding light on many of the great mysteries of astronomy. Its gaze has helped determine the age of the universe, the identity of quasars, and the existence of dark energy."
Accessed 18 October 2015:
• http://hubblesite.org/the_telescope/hubble_essentials/
"Introduction to Astronomy - MIT OpenCourseWare"
Accessed 18 October 2015:
• http://ocw.mit.edu/courses/physics/8-282j-introduction-to-astronomy-spring-2006/