A stack of k transparent slabs is arranged one on top of another, having refractive indices ₁, ₂, ₃, , _k and respective thicknesses t₁, t₂, t₃, , t_k . If an object is viewed through this assembly using nearly perpendicular light, determine the equivalent refractive index of the system that would cause the image to form at the identical location.

Step-by-step solution

The apparent depth of an object viewed through a single slab of thickness t and refractive index is given by t . For a stack of k slabs, the total apparent depth is the sum of the individual apparent depths: Apparent depth = _ i=1 ^ k t_i _i If the entire assembly is replaced by a single equivalent slab of total thickness _ i=1 ^ k t_i and equivalent refractive index _ eq , its apparent depth would be: Equivalent apparent depth = _ i=1 ^ k t_i _ eq For the image to form at the identical location, the total apparent