A horizontal ray travelling along +x strikes the curve y=x²/(4a) and is reflected vertically upward. What is the magnitude of the tangent slope at the point of incidence?
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Question

A horizontal ray travelling along +x strikes the curve y=x²/(4a) and is reflected vertically upward. What is the magnitude of the tangent slope at the point of incidence?

G1 Physics · Accepted Answer

A 90° change in propagation direction requires the normal to bisect the angle between the reverse incident direction and the reflected direction. Therefore the tangent is at 45° to the x-axis and its slope magnitude is 1.