Considering the illustrations for Concave and Convex mirrors. Prove using geometry that the reflected rays reach the...

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Physics

Considering the illustrations for Concave and Convexmirrors.
Prove using geometry that the reflected rays reach the focalpoint f=R/2 in the limit as the incoming rays approach theprincipal axis.
Hint: Consider the triangle formed by the radius of curvature,principal axis, and reflected ray, and use the law of sines.

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There are two alternative methods of locating the image formedby a concave mirror The first is purely graphical and the seconduses simple algebraic analysisThe graphical method of locating the image produced by a concavemirror consists of drawing lightrays emanating from key points onthe object and finding where these rays are brought to a focus bythe mirror This task can be accomplished using justfoursimple rulesAn incident ray which is parallel to the principal axis isreflected through the focus of the mirrorAn incident ray which passes through the focus of the mirror is reflectedparallel to the principal axisAn incident ray which passes through the centre of curvature of the mirror is reflected backalong its own path since it is normally incident on themirrorAn incident ray which strikes the mirror at its vertex is reflected such that its angleof incidence with respect to the principal axis is equal to itsangle of reflectionThe validity of these rules in the paraxial approximation isfairly selfevidentConsider an object which is placed a distance See Answer

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