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JEE Main 2023 (6 Apr, Shift 1) · Refraction, Glass Slab & Apparent Depth

Refraction, Glass Slab & Apparent Depth question from JEE Main 2023 (6 Apr, Shift 1)

Q41JEE Main 2023 · 6 APR · SHIFT 1Medium

Refraction, Glass Slab & Apparent Depth

A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2.15 m2.15\text{ m} within water when sunlight is incident at angle of 30∘30^\circ with the surface of water. If swimming pool is filled to a height of 1.5 m1.5\text{ m}, then the height of the pole above the water surface in centimeters is (nw=4/3)(n_w = 4/3) ____________.

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

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Answer: 50

  1. Sunlight at 30∘30^\circ with the surface means angle of incidence i=60∘i = 60^\circ.
  2. sin⁡r=sin⁡60∘4/3=338=0.650\sin r = \frac{\sin 60^\circ}{4/3} = \frac{3\sqrt{3}}{8} = 0.650, so tan⁡r=0.6500.760=0.854\tan r = \frac{0.650}{0.760} = 0.854.
  3. Shadow at bottom =htan⁡60∘+1.5tan⁡r= h\tan 60^\circ + 1.5\tan r, where hh = height of pole above water.
  4. 2.15=1.732h+1.5(0.854)=1.732h+1.281⇒h=0.8691.732≈0.50 m2.15 = 1.732h + 1.5(0.854) = 1.732h + 1.281 \Rightarrow h = \frac{0.869}{1.732} \approx 0.50\text{ m}
  5. So the height above water is 50 cm50\text{ cm}.
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