JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Geometrical Optics

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A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2.15 m within water when sunlight is incident at an angle of

3 0^{\circ}

with the surface of water. If swimming pool is filled to a height of 1.5 m, then the height of the pole above the water surface in centimetres is (

n_{w} = 4/3

)

Answer: 50

Solution

Apply Snell's law at the water surface:

sin 6 0^{\circ} = \frac{4}{3} sin r \Rightarrow sin r = \frac{3 3}{8}

This gives

tan r = \frac{3 3}{37}

From the geometry of the shadow:

x 3 + 1.5 tan r = 2.15

Substituting:

x 3 = 2.15 - 1.5 \times \frac{3 3}{37}

x = \frac{2.15}{3} - \frac{4.5}{37} = 1.241 - 0.739 = 0.502

\approx 0.50

m = 50 cm

JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Integer answer

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