A transparent cube of 0.21 m edge contains a small air bubble. Its apparent distance when viewed through one face of the cube is 0.10 m and when viewed from the opposite face if 0.04 m. The actual distance of the bubble from the second face of the cube is

Question

A transparent cube of 0.21 m edge contains a small air bubble. Its apparent distance when viewed through one face of the cube is 0.10 m and when viewed from the opposite face if 0.04 m. The actual distance of the bubble from the second face of the cube is (A) 0.06 m (B) 0.17 m (C) 0.05 m (D) 0.04 m

Tardigrade Admin · Accepted Answer

textRefractive index =( textreal depth/ textapparent depth) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/845e309174becdf1f222c73e78ef2058-.png" /> ∴ (x/0.04)=(0.21-x/0.10) ⇒ 0.21× 0.04-x× 0.04=0.10x ⇒ x=(0.21× 0.04/0.14) =0.06 m

Q. A transparent cube of $0.21 m$ edge contains a small air bubble. Its apparent distance when viewed through one face of the cube is $0.10 m$ and when viewed from the opposite face if $0.04 m$ . The actual distance of the bubble from the second face of the cube is

0.06 m

0.17 m

0.05 m

0.04 m

$Refractive index = \frac{real depth}{apparent depth}$

$∴ \frac{x}{0.04} = \frac{0.21 - x}{0.10}$
$\Rightarrow 0.21 \times 0.04 - x \times 0.04 = 0.10 x$
$\Rightarrow x = \frac{0.21 \times 0.04}{0.14}$
$= 0.06 m$

Q. A transparent cube of 0.21m edge contains a small air bubble. Its apparent distance when viewed through one face of the cube is 0.10m and when viewed from the opposite face if 0.04m. The actual distance of the bubble from the second face of the cube is