Question

A transparent cube contains a small air bubble. Its apparent is $2cm$ when seen through one face and $5cm$ when seen through other face. If the refractive index of the material of the cube is $1.5$, the real length of the edge of cube must be

• A. $7cm$
• B. $7.5cm$
• C. $10.5cm$
• D. $\frac{14}{3}cm$

Answer 1

The correct option is C $10.5cm$

When viwed through (1),

$\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$

$\frac{1}{2}-\frac{1.5}{u}=\frac{0.5}{\infty }$ ($R=\infty$ ,plane)

$\frac{1}{2}=\frac{1.5}{u}$

$u=3cm$

When viewed through (1),

$\frac{n_2}{v}-\frac{n_1}{u}=\frac{n_2-n_1}{R}$

$\frac{1}{5}=\frac{1.5}{L-u}$

$L-u=7.5$

$L=7.5+3=10.5cm$