Suppose I have a Gaussian laser with a width $w$ and an intensity $I$ defined as $P/\pi w^2$, where $P$ is the laser power. If I shine the laser beam onto a convex surface with a radius of curvature $r$, would the effective intensity of the laser change due to this curved surface having a larger effective area under the beam than for a flat surface?
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Intensity is defined as the power through a unit area. In other words, it is the amount of energy that arrives per unit area, per unit time.
Therefore, over a larger surface area, the intensity of the light (laser) will be reduced at any given point. This means if you were to shine the laser over a convex surface as oppose to a flat surface, the intensity at any point will be smaller since the amount of area is increased.
A good example of this generalized for any light source, is by considering the seasons on earth (earth is also a convex surface). Many people confuse the temperatures of the seasons being due to the distance of the earth from the sun. But in reality, because the earth has a tilt, when this tilt is pointing toward the sun, the amount of light strikes a smaller area and there is more direct sunlight per unit area making it warmer, whereas in winter the tilt is in the opposite direction and so light strikes a greater area making it cooler.
