Snells Law

  • Thread starter jegues
  • Start date
  • #1
1,097
3

Homework Statement



See figure attached for problem statement.

Homework Equations





The Attempt at a Solution



I'm getting a disagreement in my equations so I must be doing something wrong.

We have two unknowns,

[tex]n_{1},\theta_{2}[/tex]

My first equation,

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

my second equation (This is where I think I am misunderstanding something)

Since it is experiencing total internal reflection,

[tex]\theta_{2} = arcsin\frac{n_{1}}{n_{2}}[/tex]

Or in other words,

[tex]sin\theta_{2} = \frac{n_{1}}{n_{2}}[/tex]

If I plug this into my first equation I get an inconsistency because,

[tex]sin\theta_{1} \neq 1[/tex]

What am I doing wrong?
 

Attachments

  • SNELLQ.JPG
    SNELLQ.JPG
    31.2 KB · Views: 344

Answers and Replies

  • #2
ehild
Homework Helper
15,543
1,912
Find the angle of incidence at the exit point of the ray. That should be greater than the critical angle so that internal reflection happen.

ehild
 
  • #3
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,368
1,035

Homework Statement



See figure attached for problem statement.

Homework Equations





The Attempt at a Solution



I'm getting a disagreement in my equations so I must be doing something wrong.

We have two unknowns,

[tex]n_{1},\theta_{2}[/tex]

My first equation,

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

my second equation (This is where I think I am misunderstanding something)

Since it is experiencing total internal reflection,

[tex]\theta_{2} = arcsin\frac{n_{1}}{n_{2}}[/tex]  This should be:  90° ‒ θ2= arcsin(n1/n2),
which is: sin(90° ‒ θ2) = cos(θ2) = (n1/n2)


Or in other words,

[tex]sin\theta_{2} = \frac{n_{1}}{n_{2}}[/tex]

If I plug this into my first equation I get an inconsistency because,

[tex]sin\theta_{1} \neq 1[/tex]

What am I doing wrong?

See comment in red above.
 
  • #4
1,097
3

Related Threads on Snells Law

  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
10
Views
1K
  • Last Post
Replies
4
Views
3K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
10
Views
5K
  • Last Post
Replies
6
Views
929
  • Last Post
Replies
5
Views
11K
Replies
2
Views
1K
  • Last Post
Replies
1
Views
2K
Top