The angle of incidence equals the angle of reflection. Always.
If the surface is curved, this is still true.
Now for some caveats.
1. If the "beam" has zero width, then there really is no complication. Measure angles relative to the line perpendicular to the surface and in the plane of incidence at the point the beam strikes the surface and everything works out perfectly.
2. If the beam has a finite width, then everything still works out, but the beam strikes the surface at more than one point and the reflected beam goes away from the surface at more than one point but at each point, the angle of incidence equals the angle of reflection, but the angle of incidence is different at each point on the curved surface. Still, at each point, one measures from the perpendicular to the surface at that point, just as described above.
Some more technical stuff.
We may say a beam has zero width if the width of the beam is very much smaller than the radius of curvature of the surface measured at the place where it strikes the surface.
Under any circumstances, the beam reflected from a curved surface will spread, i.e. be dispersed at a range of angles relative to the incoming beam and that range depends on the radius of curvature of the reflecting surface. As mentioned above, this is small if the beam is narrow, but if you are observing reflection far enough from the reflecting surface, one can observe the spread.
All this assumes "ray optics" where the sizes of the beam diameter and the radius of curvature are large compared to the wavelength of the light. It all gets more complicated otherwise.
curved
The law of reflection is valid for any ray of light. So it is also valid for curved and flat surfaces. For curved surfaces, the normal is taken as the normal to the tangent of the point where the light ray hits the surface.
Because the spoon is curved inward so your reflection appears to be upside down.+++For an explanation look up the principles of concave mirrors.
Very good question. To make a body to move along a curved path it has to be massive. But photon, the quantum of light, is having zero rest mass and even in motion negligible mass. If the particle is charged one, it can be driven along a curved path as in the case of charged particle in a magnetic field. But photon is charge less. But light can be bent. As light falls on a glass prism, then the out coming light is found to be deviated towards the base of the prism. By using the phenomenon of total internal reflection, light is easily taken through the optical fibres now a days. Light can be assumed to be along a curved path as if we see that light passes through curved optical fibre. But the reality is not so. With the idea of gravitational lens, of course, light can go along a curved path.
The curved path is called a trajectory
because that's the rule. angle of incident ALWAYS = angle of reflection.
Those angles are equal at the point where a ray of light hits the mirror,regardless of the shape of the mirror.
Whatever the shape of the mirror the angle of reflection equals the angle if incidence of the ray at the point where the ray hits.
Yes. Although it may not seem like it when the surface is curved, the angles are taken in respect to the "tangent" (derivative) to the curve.
curved
The law of reflection is valid for any ray of light. So it is also valid for curved and flat surfaces. For curved surfaces, the normal is taken as the normal to the tangent of the point where the light ray hits the surface.
Neither, it depends on what you are trying to accomplish.
The ceiling of conference hall are curved so that after the light reflection reaches all corners of the hall, the room becomes bright.
Because the spoon is curved inward so your reflection appears to be upside down.+++For an explanation look up the principles of concave mirrors.
five
they are made out of reflective material, and just reflect in a different direction
No. I don't honestly know why just that it doesn't because my teacher said so but she could be wrong. Some teachers can be pretty stupid. Yes of course. Don't spew nonsense. It's a LAW. All you have to do to prove this point, is to draw a semi-major axis, aka tangent to any point on the curved surface, draw the normal, then reflect the incoming ray. If you do this for parallel rays coming onto the curved surface, you'll realize that the reflected rays converge at one point, the focal point, because the curved mirror acts as a lens as well.