k transparent slabs are arranged one over another. The refractive indices of the slabs are μ 1 , μ 2 , μ 3 , … μ k and the thickness are t 1 , t 2 , t 3 , … t k . An object is seen through this combination with nearly perpendicular light. Find the equivalent refractive index of the system which will allow the image to be formed at the same place.

k transparent slabs are arranged one over another. The refractive indices of the slabs are μ₁, μ₂, μ₃, … μ_k and the thickness are t₁, t₂, t₃, … t_k. An object is seen through this combination with nearly perpendicular light. Find the equivalent refractive index of the system which will allow the image to be formed at the same place.

Total number of transparent slabs= k

Thickness of the slabs= t₁, t₂, t₃, … t_k

Refractive index= μ₁, μ₂, μ₃, … μ_k

Then the shift can be written as

= . (1)

= …………(2)

1