A horizontal ray travelling along +x strikes the parabola y²=4ax and is reflected vertically upward. At the point of incidence P, what is the slope of the tangent?
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A horizontal ray travelling along +x strikes the parabola y²=4ax and is reflected vertically upward. At the point of incidence P, what is the slope of the tangent?

G1 Physics · Accepted Answer

The incident and reflected propagation directions are perpendicular. The normal bisects the angle between the reverse incident direction (−x) and the reflected direction (+y), so the normal has slope −1 and the tangent has slope +1.