A jar of height h is filled with a transparent liquid of refractive index `mu ` (See figure). At the centre of the jar on the bottom surface is a dot. Find the minimum diameter of a disc, such that when placed on the top surface symmertically aobut the centre , the dot is invisible

Explanation

`rArr` Suppose required minimum diameter of given disc is d. Here for the light rays emanating from point like object O and then becoming incident on water surface (from inside), if `i gt C,` then that object O wil not be see by the observer while observing from outside the water. (Where C = critical angle for water to air) Suppose angle i in the figure is equal to C . Now, according to formula.
`sin C = 1/mu`
`therefore sin i = 1/mu ( because C = i)`
From the figure,
`tan i =(d/2)/(h)`
`therefore d/2 = h tan i ......(1)`
Now, sin ` i = 1/mu`
`therefore cos i = sqrt(1 sin ^2i) = sqrt(1 - 1/(mu^2)) = (sqrt(mu^2 -1))/(mu)`
`therefore tan i = (sin i)/(cos i) = (1/u)/(sqrt(mu^2-1)/(mu))=(1)/(sqrt(mu^2-))`
`therefore` From equation (1),
`d/2 = h xx (1)/(sqrt(mu^2 - 1))`
`therefore d = (2h)/(sqrt(mu^2-1))`
Above equation gives required result.