A cylindrical vessel, whose diameter and height both are equal to 30 cm, is placed on a horizontal surface and a small particle P is placed in it at a distance of 5.0 cm from the centre. An eye is placed at a position such that the edge of the bottom is just visible (see figure 18-E8). The particle P is in the plane of drawing. Up to what minimum height should water be poured in the vessel to make the particle P visible ?

Explanation

If we pour water in vessl, refraction will take place at air and water interface.
Applying Snell's law at A, we get `1.sin 45^(@) = 4/3 sintheta`
Here, `theta` is the angle which the incidence ray of light makes with the normal.
`rArr1((1)/(sqrt2))= 4/3sinthetarArr sintheta=3/(4sqrt2)`
`tan theta= 3/(sqrt(16xx2-9))=3/(sqrt(23))`
`rArr In DeltaAPM,`
`tan theta = 3/sqrt(23)=(PM)/(AM) = (5+x)/h=(5+h-15)/h`
`3/sqrt(23)=(h-10)/h rArr 3h=hsqrt(23)-10sqrt(23)`
`h=((10sqrt(23))/(sqrt(23)-3))cm`
Hence, water should be poured upto height `(10sqrt (23))/(sqrt23-3) cm` to make the particl 'P' visible.