Reflection around normal with radians

Hello,

I need to reflect an incidence vector around a normal. The hypotenuse of the incidence vector is a fixed value, and I have the radian value of the angle it takes. I also have the length of the normal, and the corresponding radian value. Is there a way I can calculate the refraction vector in radians? A friend told me I could use $\displaystyle R = -2(N*I) - I$, but this does not produce the correct results.

Thanks in advance for your help.

Edit:

Apologies if I am being unclear. I have an object with speed 'x', traveling at angle ø. It collides with the internal edge of a circle at position (y, z). The normal is then, therefore, $\displaystyle atan( (y - circle midpoint y) / (z - circle midpoint z))$. How can I then find out the resultant vector if the object is to 'bounce' off this point?