We present new UBVI _ { c } CCD photometry of the young open clusters Trumpler 14 ( Tr 14 ) and Trumpler 16 ( Tr 16 ) in the \eta Carina nebula .
We also identify the optical counterpart of Chandra X-ray sources and Two Micron All Sky Survey point sources .
The members of the clusters were selected from the proper motion study , spectral types , reddening characteristics , and X-ray or near-IR excess emission .
An abnormal reddening law R _ { V,cl } = 4.4 \pm 0.2 was obtained for the stars in the \eta Carina nebula using the 141 early-type stars with high proper motion membership probability ( P _ { \mu } \geqq 70 \% ) .
We determined the distance to each cluster and conclude that Tr 14 and Tr 16 have practically the same distance modulus of V _ { 0 } - M _ { V } = 12.3 \pm 0.2 mag ( d = 2.9 \pm 0.3 kpc ) .
The slope of the initial mass function was determined to be \Gamma = -1.3 \pm 0.1 for Tr 14 , \Gamma = -1.3 \pm 0.1 for Tr 16 , and \Gamma = -1.4 \pm 0.1 for all members in the observed region for the stars with \log m \geqq 0.2 .
We also estimated the age of the clusters to be about 1 – 3 Myr from the evolutionary stage of evolved stars and low-mass pre-main-sequence stars .