1
$\begingroup$

What is the equation describing the shape of a mirror with the property that light rays from a point source placed at the origin will be reflected in a beam of rays parallel to the x-axis?

My answer

The mirror of course would be a spherical section. Further, since convex mirror converges a beam of rays to a point, and a concave mirror diverges, the mirror will be a concave one.

But how to obtain the shape of the mirror in terms of focus (a,0), say, of a parabola?

$\endgroup$
2
$\begingroup$

The spherical mirror is only approximately the correct answer. The property you want is only given by a parabolic mirror.

From the Wikipedia page I can quote that the relation is $4 f y = x^2$ where $f$ is the distance of the focus to the origin of the parabola.

Your focus is at $(a, 0)$, so the equation would be $4 a x = y^2$. You can solve that equation for $y$ and have a function $y = f(x) = \sqrt{4 a x}$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.