A glass cube of length 21 cm has a small air bubble trapped inside. When viewed normally from one face, its apparent distance is 8 cm. When viewed normally from the opposite face, its apparent distance is 6 cm. The refractive index of the glass and the actual distance of the air bubble from the first surface respectively are:

Step-by-step solution

The refractive index n of the glass and the actual distance d₁ of the air bubble from the first face must be determined. The total thickness of the glass cube is L = 21 cm . When viewed normally from the first face, the apparent distance is 8 cm , giving the relation for apparent depth: n = d₁ 8 , so d₁ = 8n . When viewed from the opposite face, the apparent distance is 6 cm , and the actual distance from that face is d₂ = 21 - d₁ . Using the apparent depth formula again: n = 21 - d₁ 6 , so 21 - d₁ = 6n . Substitut