Question

'$n$' transparent slabs of refractive index $1.5,$ each having thickness $1cm,2cm,3cm....toncm$ 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 $5cm$ then the value of '$n$' is ....

• A. $5$
• B. $4$
• C. $3$
• D. $6$

Answer 1

Answer: (A), (B)

The correct options are
A $5$
B $4$

As the refractive index of all the slabs are 1.5 so they may be a considered a single slab with thickness summed up
Summed up thickness of n slabs $=1+2+3+...+n$
$=\frac{n(n+1)}{2}$
Given, for small angle of incidence,
shift of object $=(1-\frac{1}{\mu })\Delta t$

so, $\Rightarrow 1cm=(1-\frac{1}{1.5})\frac{n(n+1)}{2}$

$\Rightarrow 6=n(n+1)$

$\Rightarrow n^2+n-6=0$

$\Rightarrow n^2+3n-2n-6=0$

$\Rightarrow n(n+3)-2(n+3)=0$

$\Rightarrow (n+3)(n-2)=0$

So, $n=-3$ or 2

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