Firstly, I'm sorry if this is incorrect or if there is a specific place for such questions but as this is neither a problem posed to me, nor something that has been taught - I have little background with which to work with but it is something I need to do for my ERT and 2 maths teachers have been unsuccessful in explaining it. My dilemma is how to find the incident angle on a convex lens (so any portion of a circle) on the first side, and on the internal surface as it leaves the lens. I was slightly confused about the normal vs. tangent lines to the curve. So firstly, is the angle of incidence measured to a normal that is 90* (So, vertically through the lens) or the tangent at that angle of the curve (from the centre of the circle)? And then how do you find the angle of incidence internally at the second surface interface given the first angle of refraction? I know how to find the angle of incidence given the angle of the interface, such as on a prism... but how do you find it for a circle, and can it be done with the derivative of the function of a circle? (Or do I also misunderstand the use of derivatives??) I'm pretty lost on all of this. :/ The only thing my teacher could give me was a triangular prism (which could be drawn inside the circle) where given the angle of refraction was 27 degrees. Then a+b = 180* therefore 27* + b + c2 = 180*. Where a is the top of the prism, b is the midpoint in line with a, but lower than and between the first interface and the exit interface. Unfortunately I don't know what C refers to as his diagram is so small and he gave no other notes.