question_answer 58)

  A circular disc of radius *R' is placed co-axially and horizontally inside an opaque hemispherical bowl of radius 'a', Fig. 6(EP).9. 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 p. and the near edge of the disc becomes just visible. How far below the top of the bowl is the disc placed ?

Answer:

                    m Fig. 6(EP).9, we have shown an opaque hemispherical howl of radius a with centre 0. A circular disc of radius R with centre C is placed co-axially and horizontally inside the bowl. We have to calculate OC = d. AMA' is the direction of incident ray before liquid is filled in the bowl. When liquid of refractive index p. is filled in the bowl, the near edge B of the disc just becomes visible. Here, BM is the incident ray, which is refracted along MA'. N/N? is normal to the horizontal surface of liquid in the bowl. i is the angle of incidence and r =  is the angle of refraction. As refraction occurs at M in going from denser to rarer medium, therefore, according to Snell's law                                               ?(i   Now,                                 and Putting in (i),we get         or On simplifying, we get