Mirror image around a curved line (say a parabola $y^2 = 4x$)
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I wanted to know how we can find the mirror of an object across a curved line in the $XY$ plane, like a parabola. Along a straight line in the $XY$ plane the procedure is intuitive enough. But I assume we will have to see how the object is distorted, magnified/demaginified etc. for a curved mirror?
Would the way we think about this be similar to how we think about objects placed in front of spherical mirrors?
Is there a general, coordinate geometric procedure to do this for a mirror of any shape?
analytic-geometry
asked Jan 17 at 13:06
learninglearning
4081413
$endgroup$
add a comment |
$begingroup$
I wanted to know how we can find the mirror of an object across a curved line in the $XY$ plane, like a parabola. Along a straight line in the $XY$ plane the procedure is intuitive enough. But I assume we will have to see how the object is distorted, magnified/demaginified etc. for a curved mirror?
Would the way we think about this be similar to how we think about objects placed in front of spherical mirrors?
Is there a general, coordinate geometric procedure to do this for a mirror of any shape?
analytic-geometry
asked Jan 17 at 13:06
learninglearning
4081413
$endgroup$
1
$begingroup$
I would think of finding the symmetrical of a point $P$ on the line perpendicular to (the tangent to) the parabola, at the same distance of $P$. Could that work?
$endgroup$
– Matteo
Jan 17 at 13:43
add a comment |
$begingroup$
I wanted to know how we can find the mirror of an object across a curved line in the $XY$ plane, like a parabola. Along a straight line in the $XY$ plane the procedure is intuitive enough. But I assume we will have to see how the object is distorted, magnified/demaginified etc. for a curved mirror?
Would the way we think about this be similar to how we think about objects placed in front of spherical mirrors?
Is there a general, coordinate geometric procedure to do this for a mirror of any shape?
analytic-geometry
asked Jan 17 at 13:06
learninglearning
4081413
$endgroup$
I wanted to know how we can find the mirror of an object across a curved line in the $XY$ plane, like a parabola. Along a straight line in the $XY$ plane the procedure is intuitive enough. But I assume we will have to see how the object is distorted, magnified/demaginified etc. for a curved mirror?
Would the way we think about this be similar to how we think about objects placed in front of spherical mirrors?
Is there a general, coordinate geometric procedure to do this for a mirror of any shape?
analytic-geometry
analytic-geometry
asked Jan 17 at 13:06
learninglearning
4081413
asked Jan 17 at 13:06
learninglearning
4081413
asked Jan 17 at 13:06
learninglearning
4081413
asked Jan 17 at 13:06
learninglearning
4081413
asked Jan 17 at 13:06
learninglearning
4081413
4081413
1
$begingroup$
I would think of finding the symmetrical of a point $P$ on the line perpendicular to (the tangent to) the parabola, at the same distance of $P$. Could that work?
$endgroup$
– Matteo
Jan 17 at 13:43
add a comment |
1
$begingroup$
I would think of finding the symmetrical of a point $P$ on the line perpendicular to (the tangent to) the parabola, at the same distance of $P$. Could that work?
$endgroup$
– Matteo
Jan 17 at 13:43
1
1
$begingroup$
I would think of finding the symmetrical of a point $P$ on the line perpendicular to (the tangent to) the parabola, at the same distance of $P$. Could that work?
$endgroup$
– Matteo
Jan 17 at 13:43
$begingroup$
I would think of finding the symmetrical of a point $P$ on the line perpendicular to (the tangent to) the parabola, at the same distance of $P$. Could that work?
$endgroup$
– Matteo
Jan 17 at 13:43
add a comment |
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$begingroup$
I would think of finding the symmetrical of a point $P$ on the line perpendicular to (the tangent to) the parabola, at the same distance of $P$. Could that work?
$endgroup$
– Matteo
Jan 17 at 13:43