The problem involves finding the equation of a curved mirror that reflects light rays emanating from the origin parallel to the x-axis. This is framed within the context of second-order ordinary differential equations (ODEs).
The discussion is ongoing, with participants seeking clarification on the relationships between the equations involved and how to proceed from the established geometric conditions to formulating an ODE. Some participants express understanding of certain aspects while still grappling with the overall formulation.
There is a noted lack of clarity on how to connect the geometric relationships to the creation of an ODE, and participants are exploring the implications of equal angles in the context of reflection.
<br /> <br /> How do I come up with this information my self and how do you know the the origin to the point on the curve has equation y= f(x_0)x/x_0?HallsofIvy said:Let y= f(x) be the equation of the mirror. At point (x_0, f(x_0)), the tangent line to the curve is given by y= f'(x_0)(x- x_0)+ f(x_0)[/tex]. The line parallel to the x-axis has equation y= f(x_0) and the equation of the line from the origin to the point on the curve has y= f(x_0)x/x_0.<br /> <br /> To "reflect from the mirror" those two lines must make equal angles with the tangent line.