# Snell's law problem about the angle of a wave and the coast

• Nightsheron
In summary, the conversation discusses various scenarios involving waves approaching a coast at different angles and orientations. The first question involves calculating the angle of the wave offshore using a formula and converting bearings to azimuth. The second question uses a similar method to find the angle of the wave offshore. However, the third question presents confusion as the method does not work for both angles. The fourth question is straightforward, while the fifth question involves using diagrams and concepts of orthogonal projection to solve.
Nightsheron

## Homework Statement

First question:
The waves are approaching at an bearing of N70W, and at N50W, to a coast with a N13ºE orientation. What is the angle of the wave offshore?
Answer: 7 degrees and 27 degrees.

Second question:
The wave is approaching at an angle of 135º. The coast is at 305º. What is the angle of the wave offshore?
Answer: 80 degrees.

Third question (now the total confusion):
The beach is facing north-south. The wave is approaching at an angle of 277º, and 230º. What is the angle of the wave offshore?
Answers: 7º and 40º.

Fourth question:
The wave is breaking in a coast with a East-West orientation, having a N10E bearing. What is the breaking angle?
Answer: 10º.

Fifth question:
What is the incidence angle on open waters of a wave with a bearing of 130º, in a coast with a direction of 80º?

## Homework Equations

This is the formula we used at class:
Velocity of the wave offshore (as it is coming from the ocean) / Velocity of the wave when it is breaking = Sine of the angle of the wave offshore (as it is coming from the ocean) / Sine of the angle of the wave when it is breaking

## The Attempt at a Solution

First question:
Here's how I THINK the answer could have been achieved. I am just to convert the N70W to azimuth; it becomes 290, then I subtract 90 degrees until I get to a angle that is within 90º of the other one. Then I can subtract, that is, 20-13=7. But I do not know if this is the right method.

Second question:
My thinking: 305-90= 215 ; 215-135=80

Third question:
I don't know. If I use the above method, it works for the first angle, but the second angle would give me 50 degrees instead.

Fourth question:
This one seems straightforward but I am not going to assume anything!

Fifth question:
I don't know neither the answer nor how it is supposed to be done.

My teacher talked something about a projection, is it a orthogonal projection or...? He also talked something about drawing a perpendicular to a coast?
I can't find anything on the web that is similar so I can figure it out. PLEASE help. If someone could give me the name of this kind of exercise, and some explained examples, I could try, but I haven't found much after hours of searching.

I have tried solving this, but I don't know if I am right or not.

I've been pulling my hairs for these ones! I have spent many a good hours on this, almost the entire day actually. If it didn't come through as I wrote the post, note the time here in Portugal is 4:30 AM. :(

Sorry if the wording seems odd, as I have translated it from Portuguese.

Thanks very much.

Seems like some careful diagrams would help.

I made a diagram for one of the cases, I'll make some more, but am I on the right track so far? I haven't got much of a clue to be honest with you.

SEE DIAGRAM IN ATTACHMENT.

Seeing it a little different now than I was at the OP, I first drew the beach at the orientation given. (I drew it through the other quadrant as well, since the beach is not in just one quadrant right?). Then I drew the wave. Then I drew a perpendicular of the beach: this is what I don't know the reasoning behind, but I remember we did something like this in class. Explanation please? Then I just measured from one angle to the other one.

Tried to make it somewhat clean for educational purposes, maybe someone else will have this question one day. :D

#### Attachments

• Diagram number one.jpg
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Last edited:

## 1. What is Snell's law?

Snell's law is a principle in physics that describes the relationship between the angle of a wave and the angle at which it is refracted (bent) as it passes through a medium with a different density.

## 2. How does Snell's law apply to waves and the coast?

In the context of waves and the coast, Snell's law can be used to determine the angle at which a wave will be refracted as it approaches the shore, based on the angle at which it approaches the coast and the density of the water near the coast.

## 3. Why is Snell's law important for understanding waves at the coast?

Snell's law is important because it helps us predict how waves will behave as they approach the coast, which is crucial for understanding and predicting coastal erosion, wave energy, and other factors that impact coastlines.

## 4. How is Snell's law calculated?

Snell's law is calculated using the equation n1sinθ1 = n2sinθ2, where n1 and n2 are the indices of refraction for the two media, and θ1 and θ2 are the angles of incidence and refraction, respectively. This equation can be solved for any of the four variables, depending on which information is known.

## 5. What are some real-world applications of Snell's law?

Snell's law has many practical applications, including predicting the path of light through different materials, designing lenses and prisms for optical instruments, and understanding the behavior of waves in the ocean and other bodies of water.

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