Solving Refraction by Water: Exploring Fermat & Snell's Law

In summary, refraction is the bending of light as it passes through different mediums, such as air, water, or glass. Water affects refraction by slowing down the speed of light and causing it to change direction. Pierre de Fermat and Willebrord Snell were mathematicians who discovered the relationship between the angles of incidence and refraction, which is known as Snell's law. This law can be used to solve refraction problems involving water by calculating the angle of refraction using refractive indices and angles of incidence and refraction. Refraction by water can be observed in everyday life, such as when objects appear bent or closer when viewed through water. Other factors that can affect refraction by water include temperature, density,
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chrisakatibs
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1. Your car key has fallen to the bottom of a clear pool of water (n = 1.33) with a uniform depth of 3.0 m. You are standing at the edge of the pool and your eyes are a height of 1.5 m above the surface. You can see the key by staring at an angle 60o below horizontal. (A) How far is the key from the edge of the pool? (B) i. How much time does it take light reflecting off the key to reach your eyes? ii. How much time would it take the light to travel to your eyes if it traveled in a straight line (instead of refracting at the surface)? iii. How much time would it take the light to travel if it exited the water vertically, then turned and traveled directly to your eyes? iv. What do your results suggest is special about the actual path the light ray follows? This is known as Fermat’s Principle. (C) Imagine a light ray that reflects off the key, strikes the surface of the water a distance x from the edge of this pool, and then bends to travel towards your eye. How much time would it take the light to travel to your eyes in this general case? (D) Use your result from part C to find the distance x which minimizes the time it takes for the light to reach your eyes. What does this tell you about Snell’s Law?



Homework Equations



Snell's Law


3. The Attempt at a Solution
I can easily solve part a and b using algebra and snells law but I'm wondering about how to approach part c and d. thank you

 
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Please show us what you have tried so far.
 
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Thread locked.

chrisakatibs -- please check your PMs.
 

FAQ: Solving Refraction by Water: Exploring Fermat & Snell's Law

1. What is refraction and how does water affect it?

Refraction is the bending of light as it passes through different mediums, such as air, water, or glass. Water affects refraction by slowing down the speed of light and causing it to change direction.

2. Who were Fermat and Snell and what is their law?

Pierre de Fermat and Willebrord Snell were mathematicians who discovered the relationship between the angles of incidence and refraction. Their law states that the ratio between the sine of the angle of incidence and the sine of the angle of refraction is equal to a constant for a given pair of mediums.

3. How is Snell's Law used to solve refraction problems involving water?

Snell's Law can be used to calculate the angle of refraction when light passes through water. The equation is n1sinθ1 = n2sinθ2, where n1 and n2 are the refractive indices of the two mediums and θ1 and θ2 are the angles of incidence and refraction respectively.

4. Can refraction by water be demonstrated in everyday life?

Yes, refraction by water can be observed in everyday life. For example, when you place a straw in a glass of water, it appears bent due to the refraction of light as it passes from the water to the air. This is also why objects appear to be closer or larger when viewed through water.

5. What other factors can affect refraction by water?

The temperature and density of water can also affect refraction. As the temperature of water increases, its density decreases, which can cause the speed of light to change and therefore affect refraction. Additionally, the amount of impurities in the water can also impact refraction.

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