Question

A transparent cube of $15cm$ edge contains a small air bubble. Its apparent depth when viewed through one face is $6cm$ and when viewed through opposite face is $4cm$. The refractive index of material of cube is

• A. $2$
• B. $1.5$
• C. $1.6$
• D. $2.5$

Answer 1

The correct option is B $1.5$

When light enters from denser to rarer medium
$\frac{\text{real depth}}{\text{apparent depth}}=R.I\left(\mu \right)$

Let
the real depth of the object from one face be $x$
Given apparent depth from this face is $6cm$
$\frac{x}{6}=\mu$

$x=6\mu$

real depth from opposite face is $15-x$
apparent depth from opposite face is $4cm$

$\frac{15-x}{4}=\mu$

$15-x=4\mu$
Substituting
$15=10\mu$

$\mu =1.5$