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?
(A)For n=1.42,h=50cm.✓ Correct
(B)For n=1.35,h=36cm.✓ Correct
(C)For n=1.45,h=65cm.
(D)For n=1.48,h=85cm.
Answer: (A), (B)
Solution
Since STU is a plane mirror, we can consider the mirror image of the system. For the image to form at the object itself, h=2Feq where Feq is the equivalent focal length. Using the lens formula for the two interfaces: Feq1=(11.6−1)(92)+1(n−1)(9−2). Simplifying: h2=93.2−2n, giving h=1.6−n9 cm. For n=1.42: h=50 cm (A correct). For n=1.35: h=36 cm (B correct). For n=1.45: h=60 cm (C incorrect). For n=1.48: h=75 cm (D incorrect).
JEE Advanced · 2024 · 26 May 2024 · Paper 1 · One or more correct options
