Calculating Angle of Refraction Using Snell's Law

In summary, the figure shows a ray of light traveling through a gas, solid, and liquid with different refractive indices. To find the angle θ when the ray enters the liquid, the equation (n1)(sin θ1)=(n2)(sin θ2) is used. By solving for θ at each interface, the final value for θ is 20.9 degrees.
  • #1
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Homework Statement


The figure (http://i43.tinypic.com/2dt5e2e.jpg") shows a ray of light traveling through a gas (n = 1.00), a solid (n = 1.84), and a liquid (n = 1.61). What is the angle θ made by the ray as it enters the liquid?

Homework Equations


(n1)(sin θ1)=(n2)(sin θ2)

The Attempt at a Solution


(1.00) (sin 90-35) = (1.84) (sin θ)
θ = 26.4 degrees

(1.84) (sin 26.4) = (1.61) (sin θ)
θ = 30.5 degrees
 
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  • #2
(1.00) (sin 90-35) = (1.84) (sin θ)
This is wrong. The angle of incidence is the angle made on the incident ray with the normal.
 
  • #3
Would I just use sin 35 then? I'm confused. :frown:
 
  • #4
yes.
 
  • #5
Thanks! I'll try it again:

(1.00) (sin 35) = (1.84) (sin θ)
θ = 18.2 degrees

(1.84) (sin 18.2) = (1.61) (sin θ)
θ = 20.9 degrees
 
  • #6
It is correct.
 

1. What is Snell's Law?

Snell's Law, also known as the law of refraction, describes the relationship between the angles of incidence and refraction when a light ray passes through a boundary between two different media.

2. How is Snell's Law used in problem solving?

Snell's Law is used to calculate the angle of refraction when a light ray passes through a boundary between two different media. This can be applied to various problems involving light, such as the bending of a pencil in a glass of water or the formation of rainbows.

3. What are the key variables in Snell's Law?

The key variables in Snell's Law are the angles of incidence and refraction, as well as the refractive indices of the two media. The angle of incidence is the angle between the incident light ray and the normal to the boundary, while the angle of refraction is the angle between the refracted light ray and the normal.

4. How is Snell's Law derived?

Snell's Law is derived from the principle of least time, which states that light will travel through a medium in the shortest amount of time possible. By considering the different paths that a light ray can take when passing through a boundary, the relationship between the angles of incidence and refraction can be determined.

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

Snell's Law has many practical applications, such as in the design of lenses for cameras and eyeglasses. It is also used in the development of optical fibers for telecommunication and in the study of oceanography to understand the bending of light as it passes through water. Additionally, Snell's Law is important in the field of medicine for vision correction surgeries like LASIK.

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