Question

Write the basic assumptions used in the derivation of lens – maker’s formula and hence derive this expression. 

Answer 1

Basic assumptions in derivation of Lens-maker’s formula: 

(i) Aperture of lens should be small

(ii) Lenses should be thin 

(iii)Object should be point sized and placed on principal axis. 

Suppose we have a thin lens of material of refractive index n₂, placed in a medium of refractive index n₁, let o be a point object placed on principle axis then for refraction at surface ABC we get image at I₁ , 

∴ (n²/v²) - (n₁/u) = (n₂ - n₁ )/ R₁ ....(1)

But the refracted ray before goes to meet at I₁ falls on surface ADC and refracts at I₂ 

finally; hence I₁ works as a virtual object 2nd refracting surface 

∴ n₁/v - n₂/v₁ = (n₁ - n₂)/R₂ ....(2)

Equation (1) + (2) 

If u = ∞, ѵ = f 

Which is lens maker’s formula.