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JEE Main 2020 (3 Sep, Shift 1) · Refraction, Glass Slab & Apparent Depth

Refraction, Glass Slab & Apparent Depth question from JEE Main 2020 (3 Sep, Shift 1)

Q65JEE Main 2020 · 3 SEP · SHIFT 1Difficult

Refraction, Glass Slab & Apparent Depth

An observer can see through a small hole on the side of a jar (radius 15 cm) at a point at height of 15 cm from the bottom (see figure). The hole is at a height of 45 cm. When the jar is filled with a liquid up to a height of 30 cm the same observer can see the edge at the bottom of the jar. If the refractive index of the liquid is N/100, where N is an integer, the value of N is _____.

Figure

Numerical answer type. Work it out, then open the answer.

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Answer: 158

45°r30 cm level15 cmhole, 45 cm30 cm
  1. Jar diameter =30 cm= 30\text{ cm}. Empty jar: line of sight drops 45−15=30 cm45 - 15 = 30\text{ cm} over 30 cm30\text{ cm}, so it makes 45∘45^\circ with the vertical.
  2. With liquid up to 30 cm30\text{ cm}, the ray in air drops 15 cm15\text{ cm} and meets the surface 15 cm15\text{ cm} from the wall (the centre), with i=45∘i = 45^\circ.
  3. In the liquid it must reach the bottom edge: horizontal 15 cm15\text{ cm}, vertical 30 cm30\text{ cm}, so sin⁡r=15152+302=15\sin r = \frac{15}{\sqrt{15^2 + 30^2}} = \frac{1}{\sqrt{5}}.
  4. μ=sin⁡45∘sin⁡r=52=2.5=1.58\mu = \frac{\sin 45^\circ}{\sin r} = \frac{\sqrt{5}}{\sqrt{2}} = \sqrt{2.5} = 1.58
  5. So N=158N = 158.
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