Physics - Geometrical Optics Question with Solution | TestHub

Let the actual distance of the air bubble from the first surface be $x$.

The actual distance from the opposite face is $21-x$.

The apparent depth is given by the formula:

$\text{Apparent depth}=\frac{\text{Actual depth}}{\mu }$

When viewed from the first face:

$8=\frac{x}{\mu }\Rightarrow x=8\mu$

When viewed from the opposite face:

$6=\frac{21-x}{\mu }\Rightarrow 21-x=6\mu$

Adding the two equations:

$x+21-x=8\mu +6\mu$

$21=14\mu$

$\mu =\frac{21}{14}=1.5$

Substituting the value of $\mu$ in the first equation:

$x=8\times 1.5=12\text{ cm}$

The refractive index of the glass is $1.5$ and the actual distance from the first surface is $12\text{ cm}$.

Answer: $1.5,12\mathrm{cm}$