A small air bubble exists inside a transparent cube of side 15 cm each. The apparent of the bubble observed from one face is 6 cm and from the opposite face its apparent distance becomes 4 cm. Determine the real distance of the bubble from the first face and refractive index of the material of the cube.

Explanation

Let the real distance of the bubble from the first face be x cm.
`therefore "The real distance of the bubble from the opposite face"`
(15 - x ) cm
Let the refractive index of the material of the cube be `mu` .
We know if the object lies in a denser medium and eye in the rarer medium,
`mu = ("real distance")/("apparent distance")`
`therefore "In the first case", mu = (x)/(6)`
`"In the second case", mu = (15-x)/(4)`
`therefore " " (x)/(6) = (15 - x)/(4) or, 4x = 90 - 6x or, 10x = 90`
`or, " " x = 9cm and mu = (9)/(6) = 1.5`
Therefore, the real distance of the bubble from the first face 9 cm refractive index of the material of the cube is 1.5.