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Asked in CBSE AIPMT 1996 · Snell's law, slabs and apparent depth
Given: a plate t=6 cm thick with its back face silvered; the object is 8 cm in front of the plate and the image lies 12 cm behind the silvered face.
Idea: seen through the glass, the silvered face seems nearer than it is, at an apparent depth y=t/μ; the silvering then behaves as a plane mirror sitting at that apparent position.
The object stands y+8 in front of that apparent mirror, so its image lies y+8 behind it.
Measured from the front face, the image is therefore at y+(y+8)=2y+8.
The image is 12 cm behind the silvered face, which is 12+6=18 cm behind the front face.
2y+8=18, so y=5 cm.
μ=t/y=6/5=1.2
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