We present the second report of our systematic search for strongly lensed quasars from the data of the Sloan Digital Sky Survey ( SDSS ) .
From extensive follow-up observations of 136 candidate objects , we find 36 lenses in the full sample of 77,429 spectroscopically confirmed quasars in the SDSS Data Release 5 .
We then define a complete sample of 19 lenses , including 11 from our previous search in the SDSS Data Release 3 , from the sample of 36,287 quasars with i < 19.1 in the redshift range 0.6 < z < 2.2 , where we require the lenses to have image separations of 1 ^ { \prime \prime } < \theta < 20 ^ { \prime \prime } and i -band magnitude differences between the two images smaller than 1.25 mag .
Among the 19 lensed quasars , 3 have quadruple-image configurations , while the remaining 16 show double images .
This lens sample constrains the cosmological constant to be \Omega _ { \Lambda } = 0.84 ^ { +0.06 } _ { -0.08 } ( { stat . } ) ^ { +0.09 } _ { -0.07 } ( { syst . } ) assuming a flat universe , which is in good agreement with other cosmological observations .
We also report the discoveries of 7 binary quasars with separations ranging from 1 \farcs 1 to 16 \farcs 6 , which are identified in the course of our lens survey .
This study concludes the construction of our statistical lens sample in the full SDSS-I data set .