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Right. Perhaps you mis-read one of them or perhaps there are two different kinds of mirrors. If only one is right which one do you think it would be?I read that concave mirrors are part of a sphere, and concave mirrors can also be expressed in a parabola equation, but a parabola equation is expressed as #4py=x^2# and a circle as #x^2+y^2=R^2#. So the two can't be the same right?

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Are both the cases you mentioned hollowed inwards?

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Good pointActually, concave isn't related to a particular shape. Concave just means hollowed inwards.

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Drakkith

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You can think of the mirror as a small portion of the very bottom of this shape.

Rotating other conic surfaces, such as ellipses, circles, and hyperbolas, yields a differently shaped surface for each. More complicated mirrors can have a very complex surface shape that isn't simply a rotated conic section. We even have adaptive optics in professional telescopes that actively change the shape of the mirror to compensate for the effect turbulence in the atmosphere has on incoming light.

Some links:

http://en.wikipedia.org/wiki/Conic_section

http://en.wikipedia.org/wiki/Parabolic_reflector

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Philip Wood

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A small portion of a circle is pretty much indistinguishable from a (small portion of) a parabola. The posh way of showing this is to use a Taylor expansion of the circle equation. I give an elementary derivation in the thumbnail. A revolved parabola gives a paraboloid and a revolved circle gives a sphere. Hope this helps.

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A small portion of a circle is pretty much indistinguishable from a (small portion of) a parabola. The posh way of showing this is to use a Taylor expansion of the circle equation. I give an elementary derivation in the thumbnail. A revolved parabola gives a paraboloid and a revolved circle gives a sphere. Hope this helps.

So when we say that a concave mirror is a parabola and a part of a sphere, its not actually a sphere but an approximation. And the property of the light crossing the center of the sphere and reflecting back to that point is also an approximation right?

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Philip Wood

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That's right.So when we say that a concave mirror is a parabola and a part of a sphere, its not actually a sphere but an approximation.

If you try and apply it to a paraboloid, then it is an approximation. But as long as it's only a small 'shallow' portion of the parabola, (and symmetrical about the axis of the parabola), the approximation isn't too bad.And the property of the light crossing the center of the sphere and reflecting back to that point is also an approximation right?

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Drakkith

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Drakkith, that certainly true but it is just your opinion that a mirror is automatically a parabolic surface?

No. I don't know why you would think that.

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Why can we see our inverted and real image inside a concave mirror when the image is formed in front of it and not behind?

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