Question

# 'n' transparent slabs of refractive index 1.5, each having thickness 1 cm,2 cm,3 cm....to n cm are arranged one over another. A point object is seen through this combination with perpendicular light. If the shift of object by the combination is 5 cm then the value of 'n' is ....

A
5
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B
4
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C
3
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D
6
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Solution

## The correct options are A 5 B 4As the refractive index of all the slabs are 1.5 so they may be a considered a single slab with thickness summed upSummed up thickness of n slabs =1+2+3+...+n=n(n+1)2Given, for small angle of incidence,shift of object =(1−1μ)Δtso, ⇒1cm=(1−11.5)n(n+1)2⇒6=n(n+1)⇒n2+n−6=0⇒n2+3n−2n−6=0⇒n(n+3)−2(n+3)=0⇒(n+3)(n−2)=0So, n=−3 or 2As, n can not be negative. so n=2

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