My baby is 7weeks and 6days old. May I know when he will give an eye contact and smile at me.

Question

Accepted Answer

compared to their 1st month, when they only focus on objects about a foot away, babies three or four months of age have better color perception and can start to make out other objects besides faces, like toys.

by 4 months, they should also start to show more conscious behavior like reaching for their toys and smiling deliberately at you when you make eye contact.

babies might show a reflexive smile, grinning for no apparent reason, from birth, but between 4 weeks to 4 months,  they'll develop a social smile, either responding to another person or trying to get someone else to smile at them.

when the child is smiling without any interaction that is not social smile.
a social smile is reciprocal, meaning your baby smiles in response to someone else's smile. the vision as well as the brain of the child is matureing in a proper way when the child is smiling on seeing a person. it says he's able to see short distances, make sense of an object (in this case a smiling face), and produce his own smile in return. 
a social smile also boosts bonding, since it's one of the first forms of commutnication between parent and child. 
if despite your encouraging grins you don't notice a social smile by 4 months, bring it up with your pediatrician; rarely this can signal eye problems or a developmental delay.