Consider a tin can of height h as shown in the figure. A coin lies on the botttom at the centre. From the position shown you can barely see the far side of the bottom of the can. When the can is slowly filled with water of refractive index `mu`, coin is just visible when the can is full. Show that the ratio of the height to radius is
`h/r=2sqrt((mu^2-1)/(4-mu^2))`

Explanation

When vessel is filled with water, ray coming from coin, after refraction goes along inclined line of vision and hence the coin becomes visible.
By Snell's law, `musini=1xxsinr`
`mu=(r)/(sqrt(r^2+h^2))=1xx(2r)/(sqrt((2r)^2+h^2))`
`(mu^2)/(r^2+h^2)=(4)/(4r^2+h^2)`
`4r^2mu^2+mu^2h^2=4r^2+4h^2`
`(mu^2-4)h^2=4r^2(1-mu^2)`
`h^2/r^2=(4(1-mu^2))/((mu^2-4))=(4(mu^2-1))/((4-mu^2))`
`h/r=2sqrt(((mu^2-1))/((4-mu^2)))`