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A fish in a lake is at a 6.3 m distance from the edge of the lake. If it is just able to see a tree on the edge of the lake, its depth in the lake is _______ m. The refractive index of the water is 1.33.

A. 6.30
B. 5.52
C. 7.5
D. 1.55

Answer :

To find the depth of the fish in the lake, we can use the concept of refraction. The fish is able to see the tree on the edge of the lake, which means that the light rays from the tree are reaching the fish. Using Snell's law and trigonometry, we can find that the fish is approximately 5.52 m deep in the lake.

To find the depth of the fish in the lake, we can use the concept of refraction. The refractive index of water is 1.33. We know the distance of the fish from the edge of the lake is 6.3 m. The fish is able to see the tree on the edge of the lake, which means that the light rays from the tree are reaching the fish. In order to reach the fish, the light rays have to undergo refraction at the air-water interface and then travel through the water to reach the fish's eyes.

We can use Snell's law which 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. Since the fish is able to see the tree, the angle of incidence is 90 degrees. Using Snell's law, we can find the angle of refraction. Once we have the angle of refraction, we can use trigonometry to find the depth of the fish in the lake.

Let's plug the values into Snell's law: sin(90) / sin(angle of refraction) = 1 / 1.33. Solving for the angle of refraction, we find that the sine of the angle of refraction is approximately 0.7519. Taking the inverse sine of this value, we find that the angle of refraction is approximately 48.75 degrees. Now, using trigonometry, we can find the depth of the fish. tan(angle of refraction) = depth / distance from the edge of the lake. Plugging in the values, we get tan(48.75) = depth / 6.3. Solving for the depth, we find that the fish is approximately 5.52 m deep in the lake. Therefore, the answer is (B) 5.52 m.

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