B

Step 1: The equation of the reflecting surface is given as y = 2bx². We need to determine the slope of the curve to find the angle of incidence.
Step 2: Differentiate the equation to find the slope:
$$\frac{dy}{dx} = 4bx$$
Step 3: Suppose the beam of light strikes the curve at the point (x_0, y_0) where y_0 = 2bx_0^2. The slope at this point is 4bx_0.
Step 4: The angle of incidence (i) will correspond to this slope.
Step 5: By geometrical considerations, as the light reflects, it will eventually converge at a point. The nature of parabolic reflections suggests that all parallel beams will meet at the focus of the parabola.
Step 6: The focus of the parabola defined by y = 2bx² can be found using the formula for the focus of a parabola, which is (0, \frac{1}{4b}).
Conclusion: Therefore, the beam of light will converge at the point (0, \frac{1}{4b}). The closest answer based on the problem context is option B.