Finding critical angle: not sure which one is correct

[vwoods316]

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

 

[kuruman]

And your question to us is $\dots~$?

 

[Orodruin]

And your question to us is $\dots~$?

Perhaps "How do I type ° on the keyboard?"?

 

[Steve4Physics]

Hi @vwoods316. Welcome to PF. In addition to what's already been 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/

 

[kuruman]

n2=0.58

This means that light travels faster in a piece of plastic than in vacuum.

 

[vwoods316]

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?

 

[kuruman]

so would attempt two be the more correct option or way to approach the problem?

What do you think?

 

[vwoods316]

And your question to us is $\dots~$?

the question is the statement

 

[hutchphd]

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.

 

[vwoods316]

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

 

[kuruman]

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.

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.

 

[vwoods316]

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

 

[kuruman]

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?

 

[Steve4Physics]

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.

You need to undestand why the incorrect diagram (which one is it!?) is incorrect.