Finding critical angle: not sure which one is correct

In summary, the article discusses the concept of the critical angle in optics, addressing the confusion surrounding its calculation and application. It emphasizes the importance of understanding the refractive indices of different materials and the conditions under which total internal reflection occurs. The text reviews various methods for determining the critical angle and highlights common misconceptions, ultimately guiding readers toward accurate identification of the correct angle in practical scenarios.
  • #1
vwoods316
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0
Homework Statement
The critical angle for a certain piece of plastic in the air is 𝜃_𝑐 = 35.80. What is the critical angle of the same plastic it is immersed in water.
Relevant Equations
n1sin𝜃 = n2sin𝜃
arc_sin𝜃 = n2/n1
Attempt one:
1sin(35.8) = n2sin(90)
n2=0.58
1.33sin(𝜃)=0.58sin(90)
𝜃_c=25.8

Attempt two:
n1=n2/sin𝜃_c
n1=1/sin(35.8)
n1 = 1.7
sin𝜃_c = 1.33 / 1.7
𝜃_c = 51.57
 
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  • #2
And your question to us is ##\dots~##?
 
  • #3
kuruman said:
And your question to us is ##\dots~##?
Perhaps "How do I type ° on the keyboard?"? :wink:
 
  • #4
Hi @vwoods316. Welcome to PF. In addition to what's already been said...

vwoods316 said:
Homework Statement: The critical angle for a certain piece of plastic in the air is 𝜃_𝑐 = 35.80.
Do you think the light is travelling from air into plastic? Or from plastic into air?

Hint1: Why should gettting a refractive index of 0.7 makes you worry about violating the lawys of physics?

Hint2: You might want to note that the given value of critical angle has 4 significant figures. Will that affect your working? (Correct answer=yes!)

Hint3: The forum guidlines are well worth reading: https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/
 
  • #5
vwoods316 said:
n2=0.58
This means that light travels faster in a piece of plastic than in vacuum.
 
  • #6
Steve4Physics said:
Hi @vwoods316. Welcome to PF. In addition to what's already been said...


Do you think the light is travelling from air into plastic? Or from plastic into air?

Hint1: Why should gettting a refractive index of 0.7 makes you worry about violating the lawys of physics?

Hint2: You might want to note that the given value of critical angle has 4 significant figures. Will that affect your working? (Correct answer=yes!)

Hint3: The forum guidlines are well worth reading: https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/
so would attempt two be the more correct option or way to approach the problem?
 
  • #7
vwoods316 said:
so would attempt two be the more correct option or way to approach the problem?
What do you think?
 
  • #8
kuruman said:
And your question to us is ##\dots~##?
the question is the statement
 
  • #9
In addition to all the above correct comments, did you make a sketch of the setup?? That is the correct approach to any problem! It matters which is medium 1 and which is medium 2 for angles labelled ##\theta_1## and ##\theta_2##. You mixed them up.
 
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  • #10
hutchphd said:
In addition to all the above correct comments, did you make a sketch of the setup?? That is the correct approach to any problem! It matters which is medium 1 and which is medium 2 for angles labelled ##\theta_1## and ##\theta_2##. You mixed them up.
There was no value for index of refraction given in the problem, I had to solve for what it was for plastic and make the assumption that it was 1.33 for water
 
  • #11
vwoods316 said:
the question is the statement
The statement of the problem is the question to you, the student. When you ask us for help, you have to tell us what about the question addressed to you is troubling you so that we can help you with it. That's how it works.
vwoods316 said:
There was no value for index of refraction given in the problem, I had to solve for what it was for plastic and make the assumption that it was 1.33 for water
That's a correct assessment for the water. For the plastic you have two values, n = 0.58 and n = 1.7. Which one do you believe is correct and why? You have already been given several hints.
 
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  • #12
kuruman said:
The statement of the problem is the question to you, the student. When you ask us for help, you have to tell us what about the question addressed to you is troubling you so that we can help you with it. That's how it works.

That's a correct assessment for the water. For the plastic you have two values, n = 0.58 and n = 1.7. Which one do you believe is correct and why? You have already been given several hints.
1.7
 
  • #13
Good choice. That's what I would say it is for reasons already explained. So what do you think the critical angle from plastic to water is?
 
  • #14
vwoods316 said:
so would attempt two be the more correct option or way to approach the problem?
It's not a case of 'more corecct'. One attempt is correct. The other is wrong.

Only one of the following diagrams is correct. The correct diagram leads to the correct equation and the correct answer.
CRIT ANGLE.png

You need to undestand why the incorrect diagram (which one is it!?) is incorrect.
 
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FAQ: Finding critical angle: not sure which one is correct

What is the critical angle in optics?

The critical angle is the angle of incidence above which total internal reflection occurs when light travels from a denser medium to a less dense medium. It is defined as the angle at which the refracted angle reaches 90 degrees, meaning the refracted ray runs along the boundary between the two media.

How do I calculate the critical angle?

The critical angle can be calculated using Snell's law, which states that n1 * sin(θ1) = n2 * sin(θ2). For the critical angle, θ2 is 90 degrees, and sin(90) is 1. Therefore, the formula simplifies to: θc = arcsin(n2/n1), where n1 is the refractive index of the denser medium and n2 is the refractive index of the less dense medium.

What are the conditions for total internal reflection to occur?

Total internal reflection occurs when light travels from a medium with a higher refractive index to one with a lower refractive index, and the angle of incidence exceeds the critical angle. Additionally, the two media must be optically different, meaning their refractive indices must not be equal.

Can the critical angle be greater than 90 degrees?

No, the critical angle cannot be greater than 90 degrees. By definition, the critical angle is the maximum angle of incidence for which refraction can occur. If the angle exceeds this value, total internal reflection will take place instead of refraction.

How does the critical angle change with different materials?

The critical angle varies depending on the refractive indices of the two materials involved. A higher refractive index of the first medium (denser) relative to the second medium (less dense) will result in a smaller critical angle. Conversely, if the difference in refractive indices is smaller, the critical angle will be larger.

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