A research vessel is mapping the bottom of the ocean using sonar. It emits a short sound pulse called "ping" downward. The frequ
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Answer:
a) 404 m² b) apparent height = 7.5 m
Explanation:
This question is about refraction and total internal refraction.
Here I will take refractive index of air and water
Now let's look at the diagram I have attached here
At some angle A, the light from the ring (yellow point) under water will be totally internally refracted (B = 90°), which means that rays of light (yellow arrow) that make large enough angle A will not be able to escape from the water. Since we assumed that the ring is a point, there will be a critical cone of angle A with the ring at its apex which traces a circle of radius R on the surface of water, which, beyond this radius, no light could escape.
According to snell's law
At critical angle B = 90°
Therefore
With this, we can find the radius of the circle (refer to my diagram)
And with that we can find the area
Additional Problem
For apparent depth from above, we can think that, since we are accustomed to seeing light at the speed of c in air, our brain interpret light from <em>any</em> source to be traveling at c. This causes light that originated under water, which has the speed of
to appear as if it has traveled with the same duration as light with speed c
In order for this to happen our brain perceive shortened length which is the apparent depth.
To put it in mathematical term
So we get apparent depth
