Question

Refraction at a Thin Lens.

Answer 1

Fig. shows a convex lens of a material of refractive index μ₂ . The media on the two sides of the lens have refractive index μ₁ and μ₃ respectively. P is a point object placed on principal axis in medium 1 known as object space. PA is incident ray on the first surface of lens. Had there been only one surface the refracted ray AB would have met principal axis at Q₁ . For refraction at first surface

From refraction formula at a spherical surface

The refracted ray AB from first surface meets second surface of lens at B and the emergent ray BQ meets principal axis at Q. Q is final image formed by lens due to refraction at both surfaces. For refraction at second surface of lens Q₁ acts as a virtual object forming real image Q. For refraction at second surface

Adding Eqn. (1) and (2) we have

Let u and v denote the position of object P and final image Q. In terms of co–ordinate convention of signs.

u = –a; v = +b; R₁ = +c; R₂ = –d

We rewrite Eqn. (3) as

Equation (4) in the refraction formula for a thin lens. Commonly the media on both sides of lens is same i.e. μ₁ = μ₃ Eqn. (4) reduces to

This is refraction formula for a thin lens.