A thin biconvex lens, constructed from a material with refractive index ₂ , is flanked by a medium of refractive index ₁ on one side and a medium of refractive index ₃ on the opposite side. Both radii of curvature of the lens have the same magnitude R . A beam of light travelling parallel to the principal axis is incident on the lens from the medium ₁ . Determine the position where the image will be formed.

Step-by-step solution

Applying the formula for refraction at a spherical surface for the first surface: ₂ v₁ - ₁ u = ₂ - ₁ R₁ Given that the incident beam is parallel to the principal axis, u = - . For a biconvex lens, R₁ = +R . ₂ v₁ = ₂ - ₁ R For the second surface, the image formed by the first surface acts as a virtual object. ₃ v - ₂ v₁ = ₃ - ₂ R₂ For the biconvex lens, R₂ = -R . ₃ v - ₂ v₁ = ₃ - ₂ -R = ₂ - ₃ R Adding the equations for both surfaces: ₃ v = ₂ - ₁ R + ₂ - ₃ R ₃ v = 2 ₂ - ₁ - ₃ R v = ₃ R 2 ₂ - ₁ - ₃