Refraction Through Lens

Consider a thin lens enclosing a medium of refractive index u₂ and separating it from a medium of refractive index u₁ on its two sides. Let R₁ and R₂ be the radii of curvature of the two co-axial spherical surfaces and O is a point object situated on the principal axis.

An image I’ is formed by refraction at the first surface and let its distance from the pole of the first surface be equal to v’.



The rays are refracted from the second surface of the lens. The virtual image I’ may be regarded as the object for the second surface and the final image is formed at I which lies in the medium of refractive index u₁. If the distance of the final image from the pole of second surface is equal to v,



In this case the rays are passing from the medium of refractive index u₂ (i.e. lens) to the medium of refractive index u₁.

Adding (i) and (ii)



Dividing by u₁,



If the lens is placed in air u₁ = 1 and where u is the refractive index of the material of the lens.

Then,



Note: (1) It is to be remembered that these equations will hold true only for paraxial rays and for a thin lens where the thickness of the lens can be taken negligibly small as compared u, v, R₁ and R₂.

(2) While solving numerical problems, proper signs for u, v, R₁ and R₂ are to be used.

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