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

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2.5

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1.6

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1.5

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Solution

The correct option is D 1.5
When viewed from face (1)

$μ = \frac{u}{v} = \frac{x}{v} = \frac{x}{6} . . . . . . (i)$
Now when viewed from face (2)
$μ = \frac{15 - x}{v} = \frac{15 - x}{4} . . . . . (i i)$
From equation (i) and (ii) $μ = \frac{15 - 6 μ}{4} \Rightarrow μ = 1.5$ .

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

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

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Q. A small air bubble is inside a transparent cube of side length

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and of refractive index

\frac{4}{3}

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, then its apparent distance when viewed from opposite face will be

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

The correct option is D 1.5When viewed from face (1) μ=uv=xv=x6......(i) Now when viewed from face (2) μ=15−xv=15−x4.....(ii) From equation (i) and (ii) μ=15−6μ4⇒μ=1.5.

The correct option is D 1.5
When viewed from face (1)

$μ = \frac{u}{v} = \frac{x}{v} = \frac{x}{6} . . . . . . (i)$
Now when viewed from face (2)
$μ = \frac{15 - x}{v} = \frac{15 - x}{4} . . . . . (i i)$
From equation (i) and (ii) $μ = \frac{15 - 6 μ}{4} \Rightarrow μ = 1.5$ .