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 m

Question

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?
Screenshot 2026-02-08 at 9.44.10 PM.png

TestHub · Accepted Answer

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 ​ ​ F eq ​ 1 ​ = ( 1 1.6 − 1 ​ ) ( 9 2 ​ ) + 1 ( n − 1 ) ​ ( 9 − 2 ​ ) 2 h ​ 1 ​ = 9 1.2 ​ + 9 2 ( 1 − n ) ​ h 2 ​ = 9 3.2 − 2 n ​ h = 1.6 − n 9 ​ cm ​ (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

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Options:(select one or more)

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