I get the creation of alternate dark and bright fringes in the double slit light interference experiment. Where I am confused is there will be points on the screen where condition for constructive as well as destructive interference is not met. Example where path difference = 1/3 (wavelength). On those points there should be some light? how come we see only alternate dark and bright fringes and nothing in between?
It's because of the way your eyes work.
The intermediate areas are actually intermediate. The boundary between the light and dark areas is not a sharp line. But your eye doesn't pick up on that.
What you see is intensity. Leaving out the details, intensity is proportional to the sine squared of something-or-other. (It would be simpler if you projected the light onto the inside of a cylinder instead of a flat surface.)
If you look at the graph of sine-squared, it's exactly like the graph of a sine function except the frequency is doubled and the range is 0 to 1 instead of -1 to 1.
So the places where the light is maximum or minimum change slowesr, and the places in between change fastest.
So the in-between areas will look thin. Byt they're still there and you can see them if you watch for them. Your eye tends to de-emphasize threm.