Question

Ajar of height H is filled with transparent liquid of refractive index new at the centre of the jar on the bottom surface is a not find the minimum diameter of it is such that when it is placed on the top surface symmetrical about the centre the dot is invisible

Answer 1

Your question seems to be incomplete. So you can find complete question through the attached document.

As the figure,we have to find a value for 'd'.

We can write [tex]tan(i) = (d/2)/h\\d/2   = h tan (i)\\d      = 2h tan (i)------- (1)

Then we can use snell's law. Which is,

Refractive index of the medium X Sin value of the incident angle = constant

μ Sin(i) = 1 Sin (90)

μ Sin(i) = 1

Sin(i) = 1/μ----- (2)

Now we can get values for tan (i) by using above result.

tan (i) = 1/√(μ²-1) (see attached figure)

Substituting above value for equation (2),

d  = 2h*1/√(μ²-1)

d  = 2h/√(μ²-1)

Answer : d  = 2h/√(μ²-1)