Question

A bird flies down vertically towards a water surface. To a fish inside the water, vertically below the bird, the bird will appear to
A. be farther away than its actual distance
B. be closer than its actual distance
C. move faster than its actual speed
D. move slower than its actual speed

Answer 1

We use refractive index to solve the problem. From X-rays to radio waves, the notion of refractive index extends across the electromagnetic spectrum. It may also be used to describe wave phenomena like sound. The speed of sound is utilised instead of the speed of light in this situation, and a reference medium other than vacuum must be used.

Complete step by step answer:
In optics, a material's refractive index is a dimensionless number that defines how quickly light passes through it. It's written as $n = \dfrac{c}{v},$ with $c$ denoting the speed of light in vacuum and $v$ denoting the phase velocity of light in the medium. The phase velocity is the speed at which the wave's crests or phase move, which may differ from the group velocity, which is the pace at which the wave's pulse or envelope travels.

To distinguish it from formulations that utilise the speed of light in other reference medium than vacuum, the preceding definition is also referred to as the absolute refractive index or the absolute index of refraction. As a reference medium, air at a defined pressure and temperature has long been used.

Let$\mu$ be the relative refractive index of the 2 materials,
$\dfrac{{{\text{ Real Height }}}}{{{\text{ Apparent Height }}}} = \dfrac{1}{\mu }$
As a result, when observed by the fish, the bird's apparent height will be greater.
For refraction at plane surface $\dfrac{{{\mu _2}}}{v} = \dfrac{{{\mu _1}}}{\omega }$
Let
${\mu _1} = 1;{\mu _2} = \mu$
$\Rightarrow \omega = - x$
$\Rightarrow \dfrac{\mu }{{\text{v}}} = - \dfrac{1}{{\text{x}}}$
$\Rightarrow {\mathbf{v}} = - \mu {\mathbf{x}}$
For absolute value
$|{\mathbf{v}}| = \mu {\text{x}} > {\text{x}}$
Let the Speed of bird = x
Apparent speed of bird be |v|
$\therefore Speed = \mu {\text{x}}$

Hence, the correct options are A and C.

Note: Most transparent mediums have refractive indices of 1 to 2 for visible light. A few instances may be seen in the table below. As is customary, these values are measured at the yellow doublet D-line of sodium, which has a wavelength of 589 nanometers. Because of their low density, gases at atmospheric pressure have refractive indices near to one. Almost all solids and liquids have refractive indices greater than 1.3, with the exception of aerogel.