Understanding Snell's Law: Common Mistakes and Troubleshooting Tips

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The discussion centers on troubleshooting the application of Snell's Law in a problem involving total internal reflection. Participants express confusion over the equations used, particularly the relationship between the angles and refractive indices. A key point of contention is the interpretation of the angle of incidence and the critical angle, with emphasis on ensuring that the angle of incidence exceeds the critical angle for total internal reflection to occur. The inconsistency arises when substituting values into the equations, leading to a misunderstanding of the angles involved. Clarification is sought on correctly applying the equations to resolve the discrepancies in the calculations.
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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,

n_{1},\theta_{2}

My first equation,

n_{1}sin\theta_{1}=n_{2}sin\theta_{2}

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

Since it is experiencing total internal reflection,

\theta_{2} = arcsin\frac{n_{1}}{n_{2}}

Or in other words,

sin\theta_{2} = \frac{n_{1}}{n_{2}}

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

sin\theta_{1} \neq 1

What am I doing wrong?
 

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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
 
jegues said:

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,

n_{1},\theta_{2}

My first equation,

n_{1}sin\theta_{1}=n_{2}sin\theta_{2}

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

Since it is experiencing total internal reflection,

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


Or in other words,

sin\theta_{2} = \frac{n_{1}}{n_{2}}

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

sin\theta_{1} \neq 1

What am I doing wrong?

See comment in red above.
 
SammyS said:
See comment in red above.

Thank you.
 
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