in a double slit experiment, if the 2 slits are horizonal, the interference pattern will be of horizontal lines. But what about if the 2 slits are point sources. Will the interence pattern be horizonal lines or vertical lines?
If you use circular slits instead of the vertical slits we normally use in the double slit experiment then you will indeed get a similar pattern. You’ll get a pattern of horizontal fringes but they will be circular in shape. This is because generally the shape of the fringes is the same as the shape of the slit that the light passes through like for the normal double slit the fringes are vertical lines as the slit is a vertical line too.
You can see clearly that there are a few maximas on either side of the middle maxima and they are in a horizontal line and they are shaped like the slit, that is they are circular.
If the sources are very small pinholes (on the order of a few microns), the interference pattern will look as shown here. The individual fringes will be hyperbolae. Near the center of the pattern, this will approximate straight fringes, but in fact the fringes curve outward as they go farther off-axis.
It helps to realize that a system of two point sources is cylindrically symmetrical. In the illustration, the fringes get farther apart as the distance from the point between the two sources increases. When the interfering light lands on a flat screen, the spacing between the fringes increases both up/down (in the direction of the line between the two sources) and left/right.
The orientation of the resulting interference pattern doesn't depend on the shape of the sources, but on the orientation of them relative to each other (alignment). Meaning that if the sources are on top of each other, then the interference pattern is vertical. But if the sources are horizontally (left, right), the interference pattern is also horizontally. The shape of the sources is just causing the shape of the maxima (lines in the case of slits, round in the case of pinholes).