Snell's Law x2: Double-checking trig?

In summary, the given information is about a drawing with an index of refraction for glass of 1.52 and an index of refraction for surrounding carbon disulfide of 1.63. The incident angle at point A is given as 43.0° and the question asks at what angle the ray leaves the glass at point B. Using the equation n_{1}sin\theta_{1} = n_{2}sin\theta_{2} twice, the angle within the glass is found to be 47° and the angle with a normal line at point B is 43°. When the ray travels back through the glass into the carbon disulfide, the angle is found to be 39.492
  • #1
exi
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Homework Statement



In this drawing:

http://img245.imageshack.us/img245/6559/physgv8.png [Broken]

Index of refraction for glass: 1.52
Index of refraction for surrounding carbon disulfide: 1.63
Incident angle at point A: 43.0°
At what angle does the ray leave the glass at point B?

Homework Equations



[tex]n_{1}sin\theta_{1} = n_{2}sin\theta_{2}[/tex] (twice)

The Attempt at a Solution



Please double-check my conceptual understanding of this.

Part 1, as light travels through the carbon disulfide into the glass:

[tex]1.63sin43 = 1.52sin\theta_{2}[/tex]

[tex]\theta_{2} = sin^{-1}\frac{1.63sin43}{1.52}[/tex]

So Θ within the glass is 47°.

Drawn out and making a triangle with the upper left hand corner of the glass, a triangle forms with point B as one of its own points, meaning that the angle with a normal line at that point would be 180 - (90 + 47) = 43°.

Part 2, as light travels through the glass back into the carbon disulfide:

[tex]1.52sin43 = 1.63sin\theta_{2}[/tex]

[tex]\theta_{2} = sin^{-1}\frac{1.52sin43}{1.63}[/tex]

Which yields 39.4923°.

Am I going about this correctly?
 
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  • #2
Looks OK to me.
 
  • #3
hage567 said:
Looks OK to me.

Thanks for taking a peek - turned out to be correct.
 
  • #4
Looks correct to me too.
 

1. What is Snell's Law?

Snell's Law, also known as the Law of Refraction, is a principle in physics that describes the relationship between the angles of incidence and refraction for a ray of light passing through two different mediums, such as air and water.

2. 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 mediums and θ1 and θ2 are the angles of incidence and refraction, respectively.

3. Why is it important to double-check trigonometric calculations when using Snell's Law?

Since Snell's Law involves trigonometric functions such as sine, it is important to double-check calculations to ensure accuracy. Small errors in trigonometric calculations can lead to significant discrepancies in the final result.

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

Snell's Law is used in various fields such as optics, engineering, and astronomy. It is used to design lenses, determine the bending of light in a medium, and calculate the angles of light passing through a lens or prism.

5. How does Snell's Law relate to the concept of critical angle?

Snell's Law is closely related to the concept of critical angle, which is the angle of incidence at which the refracted ray is at a 90-degree angle with the normal. When the angle of incidence is greater than the critical angle, total internal reflection occurs.

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