A transparent cube of side 0.18 m has an air bubble in it. When viewed normally through one face the bubble appears to be at a distance of 0.08 m from that surface. When viewed normally through the opposite face, the distance of the bubble appears to be 0.04 m. Find the actual distance of the air bubble from the first face and refractive index of the material of the cube.

Explanation

Let .x. be the actual distance of the air bubble from one face.
Then, `n=(RD)/(AD)=(x)/(0.08)" "`......(1)
Similarly from the second face
`n=(0.18-x)/(0.04)" "`......(2)
from (1) and (2)

`(x)/(0.08)=(0.18-x)/(0.04)`
`0.04x=0.0144-0.08x`
` 0.12x=0.0144`
`therefore x=0.12m`
using x in (1) we get
`R.I=n=(0.12)/(0.08)=1.5`
Hence refractive index of the material of glass is 1.5.