Geometry in Parabola!
Consider a parabolic mirror with vertex . A light ray originating from focus of the parabola, strikes the mirror at a point such that it gets deviated by after reflection.
Now, if we draw a tangent at point to the same parabola, it intersects the tangent at vertex at point . Find (in degrees).
The image is not drawn to scale.
The answer is 75.
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1 solution
Moderator note:
That is an important property of parabolas that is very useful when dealing with reflections of lines through the foci / parallel to axis of symmetry.
Properties Used are :
P-1)- Tangent drawn at any point P of parabola , intersect at Tangent at vertex at Q , Such that Line joining Focus S and Given Point of intersection (Q) makes Right angel to the tangent.
P-2)- A ray emanating from focus goes parallel to the axis after reflection from Parabolic mirror. And Normal is angle bisectors b/w the incident ray(SP) and reflected ray , And Tangent is angle bisector b/w incident ray (SP) and perpendicular Line (PM) drawn from Point (P) to the directrix Foot (M) .
Hence Answer is ∠ O S Q = 7 5 o