Question

A transparent cube of side `210 mm` contains a small air bubble. Its apparent distance, when viewed from one face of the cube is `100 mm`, and when viewed through opposite face is `40 mm`. What is the actual distance of the bubble from the second face and what is the refractive index of the material of the cube ?

Answer 1

Let the bubble be at a distance `x` from face I. As `mu = ("real depth")/("apparent depth")`, therefore, for face
I, `mu = (x)/(100)` and for face II, `mu = (210 - x)/(40)`

`:. (x)/(100) = (210 - x)/(40) :. x = 150 mm`
`:.` Actual distance of bubble from face II `= 210 - x = 210 - 150 = 60 mm`
`mu = (x)/(100) = (150)/(100) = 1.5`