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 � 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? (A) For � = 1.42, ℎ = 50 cm. (B) For � = 1.35, ℎ = 36 cm. (C) For � = 1.45, ℎ = 65 cm. (D) For � = 1.48, ℎ = 85 cm.
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 � 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? (A) For � = 1.42, ℎ = 50 cm. (B) For � = 1.35, ℎ = 36 cm. (C) For � = 1.45, ℎ = 65 cm. (D) For � = 1.48, ℎ = 85 cm.