and in the triangle ACI, β = θ2 + γ B β – γ = θ2
According to Snell’s law, we know
n1 sin θ1 = n2 sin θ2
substituting the values of θ1 and θ2 , we get,
n1 sin(α+ β) = n2 sin(β- γ) ................. (1) If the rays move very close to the principal axis, the rays can be treated
as parallel and are called paraxial rays. Then the angles α, β and γ become very small. This approximation is called paraxial approximation.
sin (α+ β) = α+β and sin (β- γ) = β- γ Substituting in equation (1) n1 (α+ β) = n2 (β- γ) B n1 α + n1 β = n2 β – n2 γ ................(2)
since all angles are small, we can write
tan α = AN/NO = α
tan β = AN/NC = β
tan γ = AN/NI = γ
Substitute these in equation (2), we get,
n1 AN/NO + n1 AN/NC = n2 AN/NC – n2 AN/NI ............... (3)
    As the rays move very close to the principal axis, the point N coincides with pole of the interface (P). Therefore NI, NO, NC can be replaced by PI, PO and PC respectively.
    After substituting these values in equation (3), we get,
n1 /PO + n1 /PC = n2 /PC – n2 /PI
n1 /PO + n2 /PI = (n2 - n1 )/PC. ................(4)
      Equation (4) shows the relation between refractive indices of two media, object distance, image distance and radius of curvature.
The above equation is true for the case we considered.
    We can generalize equation (4) if we use the following sign convention.
  For all purposes of applications of refraction at curved surfaces and through lenses following conventions are used.
    – All distances are measured from the pole (or optic centre).
    – Distances measured along the direction of the incident light ray are taken as positive
   – Distances measured opposite to the direction of the incident light ray are taken as negative
   – The heights measured vertically above from the points on axis are taken as positive
   – The heights measured vertically down from points on axis are taken as negative.
Here PO is called the object distance (u)

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