Question

A thin convex lens having two surfaces of radii of curvature R₁ and R₂ is made of a material of refractive index μ₂. It is kept in a medium of refractive index μ₁. Derive, with the help of a ray diagram, the lens maker formula when a point object placed on the principal axis in front of the radius of curvature R₁ produces an image I on the other side of the lens.

Answer 1

Ray of light ON₁ strikes the convex lens ABCD of radii R₁ and R₂. First refraction occurs at face ABC and forms the image I₁ of the object O. The image I₁ acts as a virtual object for surface ADC that forms the image I.

On applying the condition of refractions on surfaces ABC and ADC.

For thin lens BI₁ = DI₁, and on adding equation (1) and (2).

Suppose object is at infinity and image at focus then

On applying sign convention for convex lens BC₁ = + R₁ and DC₂ = – R₂.