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(C) Let the velocity of the fish be $v_f = 8\,ms^{-1}$ (upward) and the velocity of the bird be $v_b$ (downward). The apparent velocity of the bird as

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$3$

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(C) Let the velocity of the fish be $v_f = 8\,ms^{-1}$ (upward) and the velocity of the bird be $v_b$ (downward). The apparent velocity of the bird as seen by the fish is given by $v_{b/f} = 12\,ms^{-1}$ (downward). According to the formula for apparent velocity due to refraction at a plane surface,the apparent velocity of an object in a rarer medium as seen from a denser medium is $v_{app} = \mu \cdot v_{actual}$. Here,the bird is in air $(\mu_1 = 1)$ and the fish is in water $(\mu_2 = 4/3)$. The velocity of the bird relative to the water surface is $v_b$. The velocity of the fish relative to the water surface is $v_f = 8\,ms^{-1}$. The apparent velocity of the bird relative to the fish is $v_{b/f} = v_{b,app} - v_f$. Since the bird is in air,its apparent velocity as seen from water is $v_{b,app} = \mu \cdot v_b = \frac{4}{3} v_b$. Given $v_{b/f} = 12\,ms^{-1}$ (downward),we have: $12 = \frac{4}{3} v_b + 8$ $12 - 8 = \frac{4}{3} v_b$ $4 = \frac{4}{3} v_b$ $v_b = 3\,ms^{-1}$.

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