k transparent slabs are arranged one over another. The refractive indices of the slabs are `mu_1, mu_2, mu_3, ............. mu_k` and the thicknesses 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.

Explanation

Total no of slab =k,
thickness `=t_1, t_2, t_3, …………..t_k`
Refractve index `=mu_1,mu_2,mu_3……….mu_k`
`:.The shift Dt=[1-1/mu_1]t_1+[1-1/mu_2]t_2`
`=+……[1-1/mu_k]t_k`……….i
`If murarr refractive index of combiN/Ation of slabs and image is formed at same place.
/_\t=(1-(1/mu)](t_1+t_2)..............+t_k`...............ii
`Equating i and ii we get (error)`