A glass tube having a curved surface at one face is shown, with refractive index 1.5. The centre of curvature of radius R lies inside the glass tube. If a particle is placed at P, it forms the real image at Q. Point O divides PQ such that OP = 2OQ. Find OP.
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Question

A glass tube having a curved surface at one face is shown, with refractive index 1.5. The centre of curvature of radius R lies inside the glass tube. If a particle is placed at P, it forms the real image at Q. Point O divides PQ such that OP = 2OQ. Find OP.

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G1 Physics · Accepted Answer

Step 1: Refraction at a spherical boundary: μ₂/v − μ₁/u = (μ₂ − μ₁)/R. Step 2: From air into glass, μ₁ = 1, μ₂ = 1.5, and R > 0 into glass. Let OQ = x, so OP = 2x; take u = −2x, v = +x. Step 3: 1.5/x − 1/(−2x) = 0.5/R ⇒ 2/x = 0.5/R ⇒ x = 4R. Step 4: OP = 2x = 8R. Final answer: (C) 8R.