(Modeling) Fish's View of the World The figure shows a fish's vie...

Question

(Modeling) Fish's View of the World The figure shows a fish's view of the world above the surface of the water. (Data from Walker, J., 'The Amateur Scientist,' Scientific American.) Suppose that a light ray comes from the horizon, enters the water, and strikes the fish's eye.

Assume that this ray gives a value of 90° for angle θ₁ in the formula for Snell's law. (In a practical situation, this angle woul​​d probably be a little less than 90°.) The speed of light in water is about 2.254 x 10⁸ m per sec. Find angle θ₂ to the nearest tenth.

Accepted Answer

According to Snell's law, C A divided by CB equals sine angle A divided by sine angle B or C A is the speed of light and medium. AC B is the speed of light and medium B find the value of the B if C A equals 2.3 times 10 to the eighth meters per second. CB is 1 50 times 10 to the eighth meters per second and A is 90 degrees round your answer to one decimal place. Now we have four possible answers being 38.7 38. 41.8 and 40.7 all in degrees. Let's go ahead and set up our ratios. You have C A divided by CBS equals sine angle A divided by sine angle B. Now we have C A which is 2.3 times to the eighth. Me just for a second. CB is 1.5 times tens of the eighth meters per second. And we have so angle A so sine of 90 degrees divided by A S A or B. Now we can solve for sine angle B, we can multiply our sign angle beat to the other side to get 2.3 multiplied by 10 to the eighth meters per second sign and beat divided by 1. times 10 to the eight moves per second equals degrees, which would be one. Now, we can multiply everything to the other side and divide to the other side. We get the sign angle B it equals to 1.5 multiplied by 10 to the eighth meters per second, divided by 2.3 and multiplied by 10 to the eighth meus per second. Now, we can just plug this into our calculator and take the inverse sign. So if we take inverse sign of both sides, we end up with our solution. The angle B is equals to 40.7 degrees. After plugging into a calculator, this means the answer to our problem answer D OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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