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 30 0 30^0 3 0 0 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 centimeters is (nw = 4/3) ____________
Physics · Geometrical optics · Laws of Refraction & Total Internal Reflection
JEE Mains 6 April 2023 Shift 1 Morning Shift

Question

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 30 0 30^0 3 0 0 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 centimeters is (nw = 4/3) ____________

Physics · Geometrical optics · Laws of Refraction & Total Internal Reflection

JEE Mains 6 April 2023 Shift 1 Morning Shift

G1 Physics · Accepted Answer

At the air-water surface, the incident angle with the normal is i = 60° Using Snell's law: sin i / sin r = n(water) = 4/3 So, sin r = ( 3 4 \frac{3}{4} 4 3 ​ )sin60° = 3√3/8 Therefore, tan r ≈ 0.85 If the water depth is 1.5 m, the horizontal shadow produced inside water is x = 1.5 tan r ≈ 1.275 m Total shadow length is 2.15 m, so the shadow due to the portion of pole above water is 2.15 - 1.275 = 0.875 m If y is the height above water: tan30° = y/0.875 Therefore, y = 0.875 tan30° ≈ 0.50 m = 50…