A bird is flying up at angle $s i n^{- 1} (3 / 5)$ with the horizontal. A fish in a pond looks at that bird. When it is vertically above the fish, the angle (in degrees) at which the bird appears to fly (to the fish) is $[n_{w a t e r} = 4 / 3]$

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Solution

Let y-axis be vertically upward and x-axis be horizontal.

$V_{y} (a p p .) = \frac{V_{y} (r e a l)}{(\frac{1}{μ})}$ ------(1)
$V_{x} (a p p .) = V_{x} (r e a l .)$ --------(2)
We also know that
$\frac{v_{y} (r e a l)}{v_{x} (r e a l)} = tan θ$ -------(3)
$tan ϕ = \frac{V_{y} (a p p)}{V_{x} (a p p)} = \frac{4}{3} tan θ = \frac{4}{3} \times \frac{3}{4} = 1$

Ans. $45^{\circ}$

Why this question?

Caution: In case of refraction at plane surface, only the component of velocity in the direction of normal to the plane surface changes given according to the shifting formula. The component paralllel to the plane of the surface does not change.

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