Calculating Focal Length of Parabolic Mirror with 5 Rays

[J.Friedrich]

i have a parabolic mirror with equation x=-1/2y^2
there are 5 parallel rays coming into the parabolic mirror at y=2,y=1,y=0,y=-1,y=-2
(a) find the focal length


i found the equation f=D^2/(16c) where D is the diameter, and c is the depth.
this gives me a focal length of (1/2)

i was hoping some one could show me how to solve for the focal length by using the laws of reflection and the geometric properties of the problem

any help would be appreciated thanks

 

[tiny-tim]

Welcome to PF!

Hi J.Friedrich! Welcome to PF!

(try using the X² icon just above the Reply box )

i was hoping some one could show me how to solve for the focal length by using the laws of reflection and the geometric properties of the problem

You know that lines parallel to the x-axis will be reflected onto the focus …

the easiest one to go for is the one that's reflected at right-angles …

so look for the point where the tangent is at 45°.