An air bubble is trapped inside a glass cube of edge 30 cm. Looking through the face ABEH, the bubble appears to be at normal distance 12 cm from this face and when seen from the opposite face CDGF, it appears to be at normal distance 8 cm from CDGF. Find refractive index of glass and also the actual position of the bubble.

Explanation

Let the actual distance of the bubble from the face ABEH is then its actual distance from the face CDGF is 30 - x
But `mu=("Actual distance of bubble from refracting surface ")/("Apparent distance of bubble from refracting surface")`
The apparent distance of bubble from refracting surface ABEH `=(x)/(mu) , 12 = (x)/(mu ` ..... (1)
The apparent distance of bubble from refracting - surface CDGF`=(30-x )/( mu ) , 8 = (30 -x)/(mu ) `
Adding Eqs (1) and (2) ` (x)/(mu ) +(30-x)/(mu )=20`
We get `mu =1.5 `
From Eq। (1) `(x)/(mu ) =12 (or) (x)/(1.5 ) = 12 `
so `x=18 cm `
This actual position of bubble is at normal distance 18 cm from face ABEH or at a distance 12 cm from face CDGF.