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Geometrical Optics question

2020 · Shift 2 · Q43
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Geometrical Optics question

2020 · Shift 2 · Q43

JEE AdvancedPhysicsGeometrical OpticsMultiple correct+4 / −2
A beaker of radius r is filled with water (refractive index 43{4 \over 3}34​) up to a height H as shown in the figure on the left. The beaker is kept on a horizontal table rotating with angular speed ω\omegaω. This makes the water surface curved so that the difference in the height of water level at the center and at the circumference of the beaker is h (h << H, h << r), as shown in the figure on the right. Take this surface to be approximately spherical with a radius of curvature R. Which of the following is/are correct? (g is the acceleration due to gravity) JEE Advanced 2020 Paper 2 Offline Physics - Geometrical Optics Question 47 English
  1. A
    R=h2+r22hR = {{{h^2} + {r^2}} \over {2h}}R=2hh2+r2​
  2. B
    R=3r22hR = {{3{r^2}} \over {2h}}R=2h3r2​
  3. C
    Apparent depth of the bottom of the beaker is close to 3H2(1+ω2H2g)−1{{3H} \over 2}\left( {1 + {{{\omega ^2}H} \over {2g}}} \right)^{-1}23H​(1+2gω2H​)−1
  4. D
    Apparent depth of the bottom of the beaker is close to 3H4(1+ω2H4g)−1{{3H} \over 4}{\left( {1 + {{{\omega ^2}H} \over {4g}}} \right)^{ - 1}}43H​(1+4gω2H​)−1
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