A glass beaker has a solid, plano-convex base of refractive index 1.60, as shown in the figure. The radius of curvature of the convex surface (SPU) is 9 ~cm , while the planar surface (STU) acts as a mirror. This beaker is filled with a liquid of refractive index n up to the level QPR. If the image of a point object O at a height of h (OT in the figure) is formed onto itself, then, which of the following option(s) is(are) correct?
B. For n=1.35, h=36 ~cm .
Since STU is a plane mirror, we can take mirror image of the whole situation about it and final image can be assumed to be at a distance h below the base. Since object and image are at same distance from equivalent lens, hence h =2 ~F _ eq aligned & 1 ~F _ eq = ( 1.6-1 1 ) ( 2 9 )+ ( n -1) 1 ( -2 9 ) \\ & 1 h 2 = 1.2 9 + 2(1- n ) 9 \\ & 2 ~h = 3.2-2 n 9 \\ & ~h = 9 1.6- n cm aligned (1) for n =1.42, ~h =50 ~cm (2) for n =1.35, ~h =36 ~cm (3) for n =1.45, ~h =60 ~cm (4) for n =1.48, ~h =75 ~cm
Related: Physics — Ray Optics · All PYQ Banks