A fish rising vertically upward with a uniform velocity of 8 ms-1, observes that a bird is diving vertically downward towards the fish with the velocity of 12 ms-1. If the refractive index of water is \(\frac{4}{3}\) , then the actual velocity of the diving bird to pick the fish, will be _______ ms-1
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The refractive index helps relate apparent and actual velocities when observations are made across media boundaries. Always apply the refractive index in the correct direction (water to air or vice versa).
Correct Answer: 3
Solution and Explanation
When light (or observation) passes from water to air, the apparent velocity of the bird as seen by the fish is related to the actual velocity of the bird by the refractive index \( \mu \). The relationship is given as: \[ v_{\text{actual}} = \mu \times v_{\text{apparent}}. \]
Here:
- The apparent velocity of the bird, as observed by the fish, is \( v_{\text{apparent}} = 12 \, \text{ms}^{-1} \)
- The refractive index of water \( \mu = \frac{4}{3} \)
Substitute the values: \[ v_{\text{actual}} = \frac{4}{3} \times 12 = 16 \, \text{ms}^{-1}. \]
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