A circular disc of radius R is placed co-axially and horizontally inside an opaque hemispherical bowl of radius a (figure).

A circular disc of radius R is placed co-axially and horizontally inside an opaque hemispherical bowl of radius a (figure). The far edge of the disc is just visible when viewed from the edge of the bowl. The bowl is filled with transparent liquid of refractive index μ. and the near edge of the disc becomes just visible. How far below the top of the bowl is the disc placed ?

Referring to the figure, AM is the direction of in bowl, BM is the direction of the incident ray. Refracted ray in both cases is same as that along MN.     ,

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