Is short-sightedness genetic ?

Not necessarily!

A study done was done in the past by Dr Young in Alaska.  He checked the vision of 130 Eskimos who were being introduced to American society.  The parents were illiterate.  They did outdoor activities like hunting, and hardly any close work.   Only 2 people out of 130 (1.5%) were found to be short sighted.  The 2 that were, only had a small amount of myopia.

Their children were all sent to mainstream education and so would have been doing a lot more studying and close work.  More than 60% of the children were short sighted!

Children with myopic parents are more likely to be myopic.  This is partly due to genetics, but could also be because of parents and children having similar lifestyles and levels of education.