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In single slit diffraction, we always assume that our waves are perpendicularly aimed towards the slit.

But what if we aimed our waves with different angles ( for example 60 deg)? If we send the waves to our slit with different angles, what will happen? will we see the same interference pattern? If you can please say in this situation, how will the wave be diffracted?

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The calculation is identical, except that the waves start with a phase difference at the entrance to the slits.

If you have perfectly narrow slits, the only difference in the pattern will be a shift of the maximum (the maximum occurs when the waves from the two slits are in phase, so there should be a maximum in the forward direction of the incident beam).

The only other thing to consider is the fact that most diffraction equations are "small angle" approximations - if you are coming in at 60 degrees to the normal that assumption is violated.

But to first order, for slits parallel to the screen, the pattern (spacing) will be unaffected by the incident angle of the light - only the position on the screen changes.

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