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A kingfisher is flying 36 m high from the water surface of a pond. A fish is 36 m deep in water from the water surface. At what depth from the water surface, the fish seems to be to the kingfisher {refractive index of water is 4/3}
- a)27 m
- b)48 m
- c)36 m
- d)12 m
Correct answer is option 'A'. Can you explain this answer?
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A kingfisher is flying 36 m high from the water surface of a pond. A f...
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To solve this problem, we can use the concept of refraction. Refraction is the bending of light as it passes from one medium to another with a different refractive index. In this case, the light travels from air (where the kingfisher is) to water (where the fish is).
Let's break down the problem into steps:
Step 1: Determine the path of light
The light from the fish travels from water to air and then reaches the kingfisher's eyes. We need to find the depth at which the fish seems to be to the kingfisher.
Step 2: Apply the Snell's law
Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two media. In this case, we can assume that the angle of incidence and the angle of refraction are small, so we can use the simplified form of Snell's law:
n1 * sinθ1 = n2 * sinθ2
where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively.
Step 3: Apply Snell's law to find the depth
In this problem, the light travels from water (n1 = 4/3) to air (n2 = 1). We know that the angle of incidence is 90 degrees (as the light is coming vertically upwards) and we need to find the angle of refraction.
Using Snell's law, we can write:
(4/3) * sin(90 degrees) = 1 * sinθ2
Simplifying the equation, we find:
(4/3) * 1 = sinθ2
θ2 = sin^(-1)(4/3) ≈ 53.13 degrees
Step 4: Calculate the depth of the fish
Now, we can use trigonometry to find the depth at which the fish seems to be to the kingfisher.
Using the tangent function, we have:
tan(θ2) = depth of fish / height of kingfisher
tan(53.13 degrees) = depth of fish / 36 m
depth of fish = tan(53.13 degrees) * 36 m ≈ 26.99 m
Rounding this value to the nearest meter gives us 27 m, which is the correct answer.
Therefore, the fish seems to be at a depth of 27 m from the water surface to the kingfisher.
Let's break down the problem into steps:
Step 1: Determine the path of light
The light from the fish travels from water to air and then reaches the kingfisher's eyes. We need to find the depth at which the fish seems to be to the kingfisher.
Step 2: Apply the Snell's law
Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two media. In this case, we can assume that the angle of incidence and the angle of refraction are small, so we can use the simplified form of Snell's law:
n1 * sinθ1 = n2 * sinθ2
where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively.
Step 3: Apply Snell's law to find the depth
In this problem, the light travels from water (n1 = 4/3) to air (n2 = 1). We know that the angle of incidence is 90 degrees (as the light is coming vertically upwards) and we need to find the angle of refraction.
Using Snell's law, we can write:
(4/3) * sin(90 degrees) = 1 * sinθ2
Simplifying the equation, we find:
(4/3) * 1 = sinθ2
θ2 = sin^(-1)(4/3) ≈ 53.13 degrees
Step 4: Calculate the depth of the fish
Now, we can use trigonometry to find the depth at which the fish seems to be to the kingfisher.
Using the tangent function, we have:
tan(θ2) = depth of fish / height of kingfisher
tan(53.13 degrees) = depth of fish / 36 m
depth of fish = tan(53.13 degrees) * 36 m ≈ 26.99 m
Rounding this value to the nearest meter gives us 27 m, which is the correct answer.
Therefore, the fish seems to be at a depth of 27 m from the water surface to the kingfisher.
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A kingfisher is flying 36 m high from the water surface of a pond. A fish is 36 m deep in water from the water surface. At what depth from the water surface, the fish seems to be to the kingfisher {refractive index of water is 4/3}a)27 mb)48 mc)36 md)12 mCorrect answer is option 'A'. Can you explain this answer?
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