Solve Water Refraction: Length of Stick's Shadow

In summary, the problem involves calculating the length of the shadow cast by an opaque stick in a pool of water when illuminated by parallel rays of sunlight at an angle of 45.0 degrees. The solution involves using Snell's law to find the angle of refraction, and then using trigonometry to calculate the length of the shadow. The incorrect solution was obtained by using the wrong angle in the calculations.
  • #1
ttiger2k7
58
0
[SOLVED] Water Refraction

Homework Statement



An opaque stick which is d = 1.93 meters tall stands vertically upright on the bottom of a pool of clear water. Parallel rays of sunlight making an angle of 45.0 degrees with the water?s surface illuminate the pool as shown. What is the length of the shadow the stick casts on the bottom of the pool?

Homework Equations



[tex]n_{a}[/tex]=1.00
[tex]n_{b}[/tex]=1.33
stick_in_water.gif


The Attempt at a Solution



So I just took

[tex]arctan(\frac{1.33}{1.00})=53.06[/tex]

And I need the angle that will form a triangle with the rod, so

[tex]90-53.06=36.94[/tex]

Then, since the shadow forms the base of a triangle, I solved for it:

[tex]tan(36.94)=\frac{opp}{adj}=\frac{opp}{1.93m}[/tex]

Adn I got that the shadow equals 1.45 m, which was incorrect. What am I doing wrong?
 
Physics news on Phys.org
  • #2
ttiger2k7 said:
So I just took

[tex]arctan(\frac{1.33}{1.00})=53.06[/tex]
Why?

Hint: Use Snell's law to find the angle the light makes upon refraction.
 
  • #3

To solve this problem, you need to take into account the refraction of light as it passes through the water. This changes the angle at which the light hits the bottom of the pool and therefore changes the length of the shadow.

To account for this, you can use Snell's Law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the indices of refraction of the two media. In this case, the angle of incidence is 45 degrees and the index of refraction of air is 1.00, while the index of refraction of water is 1.33. So we can set up the following equation:

sin(45) / sin(x) = 1.00 / 1.33

Solving for x, we get that the angle of refraction is approximately 34.6 degrees. Now, using this angle, we can calculate the length of the shadow using the same method as before:

tan(34.6) = opp / 1.93m

Solving for opp, we get that the length of the shadow is approximately 1.25m.

Therefore, the correct answer is that the length of the shadow is 1.25m. This takes into account the refraction of light as it passes through the water, giving a more accurate result.
 

Related to Solve Water Refraction: Length of Stick's Shadow

What is water refraction and how does it affect the length of a stick's shadow?

Water refraction is the bending of light as it passes through a different medium, in this case, water. This bending of light can cause objects to appear distorted or appear to be in a different position than they actually are, which can affect the length of a stick's shadow.

Why does the length of a stick's shadow change when it is placed in water?

The length of a stick's shadow changes when it is placed in water because the light rays passing through the water are bent, causing the image of the stick to appear closer to the surface of the water than it actually is. This makes the shadow appear shorter than it would if the stick was in air.

What factors can affect the amount of water refraction and the length of a stick's shadow?

The amount of water refraction and the length of a stick's shadow can be affected by several factors, including the depth and clarity of the water, the angle at which the light enters the water, and the material and shape of the stick itself.

Can the length of a stick's shadow in water be accurately measured?

Yes, the length of a stick's shadow in water can be accurately measured by taking into account the angle of light refraction and using geometric calculations to determine the actual length. These calculations can be done using trigonometric functions such as sine, cosine, and tangent.

What practical applications does understanding water refraction and shadow length have?

Understanding water refraction and shadow length can have practical applications in fields such as engineering, architecture, and photography. It can also be useful for activities such as fishing, where understanding the refraction of light in water can help determine the location of fish. Additionally, understanding water refraction can also aid in the design and construction of underwater structures, such as pools or aquariums.

Similar threads

  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
7K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
2K
Replies
1
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
16K
  • Introductory Physics Homework Help
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
3
Views
29K
Back
Top