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How to derive lens formula step by step any body plzzzz

full form?
mine is Indian School Of certificate Examination Board
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Let SPS' be a convex mirror surface separating a rarer medium of absolute refractive index n₁ from a denser medium of refractive index n₂.Let P be the centre of curvature of the surface .PC is the radius of curvature R of the surface.Let a point-object O placed on the principal axis PC produced backwards.An incident ray of light OA,after reflection at the point A on the surface,bends towards the normal CAN and goes along AI in the denser medium.Another incident ray OP falls on the refracting surface normally and goes un-deviated into the denser medium.The 2 refracted rays meet at the principal axis at I which is the real image of O.
Suppose the angle of incidence OAM=i,the angle of refraction IAC=r ,Po=-u,PI=+v and PC=+R.According to the coordinate geometry sign convention,u is -ve while v and R is +ve.Let α,β,γ b the angle made by OA,IA,Ca respect. with proncipal axis.Let h be the height of the normal AM dropped from A on the principal axis.Now,in ΔCOA,
γ=r+β........[in CIA]
or r=γ-β
by snell's law:
or n₁ sin i= n₂ sin r
or n₁i=n₂r......................[since the spherical mirror is of small aperture]
subtitute values
therefore,α=tanα =AM/Mo=Am/Po=h/-u

therefore the required eq. is
2 5 2
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