Physics

Solution:

As the refractive index of all the slabs are $1.5$ so those may be a considered as a single slab with the thickness summed up.

Summed up thickness of $n$ slabs $Δt=1+2+3+...+n$$=2n(n+1) $

Given, for small angle of incidence, shift of object: $s=(1−μ1 )Δt$

so, $⇒1cm=(1−1.51 )2n(n+1) $

$⇒6=n(n+1)$

$⇒n_{2}+n−6=0$

$⇒n_{2}+3n−2n−6=0$

$⇒n(n+3)−2(n+3)=0$

$⇒(n+3)(n−2)=0$

So, $n=−3$ or $n=2$

As, $n$ can not be negative. so $n=2$

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