EK 1001 Physics #937

[aspiringdoc09]

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The index of refraction of the water in a certain murky pond is approximately 1.4. An alligator sits 1 m below the smooth surface of the pond. The alligators view of objects above the surface is restricted to a circular window at the surface with a radius of:

A) 0.5 m
B) 1 m
C) 2 m
D) 2.5 m

If I had to guess the answer I would have put B; however, I don't understand how they came up with their answer. I thought about using Snell's law but then I realized that I didn't know either angle. The answer in the back is TOO AMBIGUOUS.

Answer Explanation: Beyond a certain radius, the angle of incidence would be so great, that the light would experience total internal reflection. This angles is the critical angle. the critical angle is found by using Snell's law which in this case is 45 degrees. They also have a diagram.

45 degrees is the ratio of the index of refraction of air (n=1) to murky pond water (1.4). How was I suppose to know that I can use Snell's law without having both angles? What words in the question were key for me to setup a ratio and obtain choice B? Now that I think about it, radii drawn in the same circle (geometry) are the same, but I wasn't thinking about the the alligator's eyes as the center point in a circle. How would you answer this question quickly and accurately without getting into theory?

 

[MT Headed]

Snells law: n1 sin(theta1)=n2 sin(theta2)

n1 = 1.4
theta1 you solve for, the angle in the water
n2 = 1
theta2 = 90 (why? angles measured from NORMAL to the interface, and any angle BEYOND 90 on the air side would be reflected back in the water)

theta1 is 45 degrees. This can be solved a variety of ways. I did it by recognizing 1.4 is the square root of 2. Thus 1/1.4 is 1/sqrt(2) is sqrt(2)/2 is 0.7, and everybody should know the sin(45)=0.7

So you have an isocoles triangle, they gave you the length of one side (1m) and ask you for the other side. Answer: 1m.


Basically this problem wants you to memorize (or derive, like i just did) the way to solve for the angle of Total Internal Reflection. I'm sure the concept is in your physics book or wikipedia.

 

[aspiringdoc09]

Snells law: n1 sin(theta1)=n2 sin(theta2)

n1 = 1.4
theta1 you solve for, the angle in the water
n2 = 1
theta2 = 90 (why? angles measured from NORMAL to the interface, and any angle BEYOND 90 on the air side would be reflected back in the water)

theta1 is 45 degrees. This can be solved a variety of ways. I did it by recognizing 1.4 is the square root of 2. Thus 1/1.4 is 1/sqrt(2) is sqrt(2)/2 is 0.7, and everybody should know the sin(45)=0.7

So you have an isocoles triangle, they gave you the length of one side (1m) and ask you for the other side. Answer: 1m.


Basically this problem wants you to memorize (or derive, like i just did) the way to solve for the angle of Total Internal Reflection. I'm sure the concept is in your physics book or wikipedia.

Thanks MT Headed. I am using EK and it briefly mentions critical angles and total internal reflection. It defines total internal reflection and and doesn't indicates memorizing the equation for the critical angle. Soon I will be switching to TPR hyperlearning, so helpfully that does a better job of explaining what I really need to know. EK tells you not to know something then hit you with questions about stuff they say don't worry about. It's confusing. I never understood physics very well. I won't forget how to approach this question type in the future.