Solve Snell's Law Problem: Determine θ

In summary, the problem involves determining the angle θ between the cone axis and the cone surface, given that a fish 30 cm below the surface of a lake can see the entire sky compressed in the cone due to refraction of light. Using the equation n1*sin(theta 1)=n2*sin(theta 2) and given values of n1=1, n2=1.33, and theta 1=90, the angle theta 2 is solved for and found to be approximately 48.75 degrees.
  • #1
haxxorboi
24
0

Homework Statement


A fish is 30 cm below the surface of a lake.
If he looks up he can see the entire sky compressed in a cone of angle θ, because of refraction of light at the water surface. (θ is the angle between the cone axis and the cone surface.) Determine θ.

Homework Equations


n1*sin(theta 1)=n2*sin(theta 2)
n1=1
n2=1.33
theta 1=90
theta 2=?


The Attempt at a Solution


sin(90)/1.33=sin(theta 2)
sin-1(0.672177943)=42.24 degrees


This doesn't seem to be the answer though...

Any help?
 
Physics news on Phys.org
  • #2
i do it i get:

1sin90 = 1.33sin(theta 2)
1 = 1.33sin(theta 2)
1/1.33 = sin(theta 2)
.7518796992 = sin(theta 2)
sin-1(.7518796992) = 48.75 degrees
 
  • #3
Man, what the heck was I doing? I did it again and I got the same answer as you, which is the correct answer...

I swear I just do things wrong 10 times in a row for no reason...

Thanks for the help!
 
  • #4
no problem...i am the same way sometimes.

sometimes you just need a clear head to straighten it out.
 

1. What is Snell's Law and why is it important?

Snell's Law is a principle in physics that describes the relationship between the angles of incidence and refraction of a wave passing through a boundary between two different mediums, such as air and water. It is important because it allows us to predict the direction of a light ray as it passes through a medium and to understand how light behaves when it encounters different materials.

2. How do you determine the angle of refraction (θ) in Snell's Law?

The angle of refraction (θ) can be determined using the formula θ = arcsin(n1/n2 * sin(θ1)), where n1 is the refractive index of the first medium and n2 is the refractive index of the second medium. θ1 is the angle of incidence, or the angle at which the light ray enters the second medium.

3. What are some examples of problems that can be solved using Snell's Law?

Snell's Law can be used to solve problems involving the refraction of light through various mediums, such as a light ray passing through a glass lens or water. It is also applicable in situations where a light ray passes through multiple mediums, such as a prism or a fiber optic cable.

4. What is the relationship between the angle of incidence and the angle of refraction in Snell's Law?

The relationship between the angle of incidence and the angle of refraction is described by Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two mediums.

5. How can I check my solution for a Snell's Law problem?

To check your solution for a Snell's Law problem, you can use a simple test called the "snell's law test". This involves checking if the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices, as stated in Snell's Law. If these ratios are equal, then your solution is correct.

Similar threads

Geometrical optics: using Snell's law, find the depth of the pool
    • Introductory Physics Homework Help
Replies
6
Views
1K
Apparent depth of an object underwater
    • Introductory Physics Homework Help
Replies
3
Views
816
Solve Snell's Law: Glass Cube Refractive Index = 1.77
    • Introductory Physics Homework Help
Replies
8
Views
4K
Statics problem on the resolution of forces
    • Introductory Physics Homework Help
Replies
18
Views
779
Prove n1<N<n2 for effective index N....
    • Introductory Physics Homework Help
Replies
3
Views
1K
Find Angle of Reflection for Snell's Law Q w/ GaP Index
    • Introductory Physics Homework Help
Replies
4
Views
2K
Fresnel Equations and Snell's Law
    • Introductory Physics Homework Help
Replies
13
Views
2K
Diffraction grating problem involving Snell's Law
    • Introductory Physics Homework Help
Replies
3
Views
5K
Red and Violet Light through a Prism (Snell's Law)
    • Introductory Physics Homework Help
Replies
6
Views
8K
Snell's law problem about a hemispherical glass ball
    • Introductory Physics Homework Help
Replies
9
Views
1K

Hot Threads

Recent Insights

Back
Top