In a pond a fish at rest sees a bird diving vertically towards water at the rate of 3m/s vertically above the fish If the refractive index of water is 4/3 .What is the actual speed of the bird
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Here is an explaination (calculus) of a more elaborate problem, take a look: https://www.zigya.com/study/book?class=12&board=tbse&subject=Physics&book=Physics+Part+II&chapter=Ray+Optics+and+Optical+Instruments&q_type=&q_topic=Refraction+at+Spherical+Surfaces+and+by+Lenses&q_category=&question_id=PHEN12057601
To find the actual speed of the bird, we need to take into account the refraction of light at the interface between air and water. The apparent speed of the bird as observed by the fish is different from its actual speed.
Let's analyze the situation using Snell's law of refraction:
Snell's law states that the ratio of the sine of the angle of incidence (θ1) to the sine of the angle of refraction (θ2) is equal to the ratio of the velocities of light in the two media. Mathematically, it can be written as:
n1 * sin(θ1) = n2 * sin(θ2),
where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively.
In this case, the bird is diving vertically, so the angle of incidence (θ1) is 90 degrees.
Given:
Refractive index of water (n2) = 4/3.
To find the angle of refraction (θ2), we can rearrange Snell's law as follows:
sin(θ2) = (n1/n2) * sin(θ1).
Since the bird is moving vertically above the fish, the angle of refraction (θ2) is also 90 degrees.
Now, let's find the actual speed of the bird:
The apparent speed of the bird, as observed by the fish, will be the component of the actual speed of the bird in the direction perpendicular to the water surface. This is because light rays from the bird will change direction due to refraction at the air-water interface.
Using trigonometry, we can find the apparent speed (Vapp) of the bird:
sin(θ2) = perpendicular component of actual speed / apparent speed.
Since sin(90 degrees) = 1, and the actual speed is given as 3 m/s, we have:
1 = perpendicular component of actual speed / apparent speed.
Therefore, the apparent speed (Vapp) of the bird is equal to the perpendicular component of its actual speed.
In this case, the bird is diving vertically above the fish, so the perpendicular component is equal to the actual speed. Hence, the apparent speed of the bird is also 3 m/s.
Therefore, the actual speed of the bird is 3 m/s.