please give me the derivation of refraction at the spherical surfaces ?

Asked by Gaurav Gaur | 30th Mar, 2013, 01:44: PM

Expert Answer:


Object at O, centre of curvature at C, virtual image at B. Pole at P. A is point of incidence. AP ’ is dropped. Refractive index of rarer medium n 1 and denser medium n 2 .

In parallaxial approximation A is very near to P thus PP’ ? 0

(Lens maker’s formula using concave and convex surfaces)

Let a ray of light from the object O incident upon a concave surface of radius R and come out of the convex surface radius R 2 . Let the rarer medium have a r.i. n 1 and denser medium n 2 .

Since the lens is thin thus P’P ? 0


OP’= -u


Radius = -R 1

Applying the Gaussian formula for concave surface,

Answered by  | 30th Mar, 2013, 02:35: PM

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