A biconvex thin lens, fabricated from a material of refractive index ₂ , separates a medium of refractive index ₁ on one face and a medium of refractive index ₃ on the other face. The two radii of curvature of the lens share an equal magnitude R . A beam of light travelling parallel to the principal axis strikes the lens from the medium ₃ . At what position will the image be formed?

Step-by-step solution

For the first refraction at the surface separating medium ₃ and the lens ₂ , the incident light is parallel to the principal axis, so the object is at infinity ( u = - ). The radius of curvature for the first biconvex surface is R₁ = +R . Using the formula for refraction at a spherical surface: ₂ v₁ - ₃ - = ₂ - ₃ R ₂ v₁ = ₂ - ₃ R For the second refraction at the surface separating the lens ₂ and medium ₁ , the image formed by the first surface acts as a virtual object. The radius of curvature for the second biconve