MC (multiple choice) question about total internal reflection

Tags:
1. Aug 30, 2015

cainko

1. The problem statement, all variables and given/known data
There is an optical fiber.A light ray enter it at i°.Total internal reflection occur at X.
What are the necessary conditions for the light ray to travel along the core of the fiber?
(I have cancelled B and D already.)
A.n1>n2 and angle i should be greater than a certain value.
C.n1>n2 and angle i should be less than a certain value.

2. Relevant equations
sinθa/sinθg=1/n; sinc=1/n;n1/n2=v1/v2

3. The attempt at a solution
For t.i.r. θ>c
r=90°-θ
r<90°-c
But I don't understand how I can determine i is greater than or less than c(certain value) because i and r are not the same?
Thank you so much!:)
cainko
(Sorry for my bad drawing)

Attached Files:

• tir.png
File size:
1.4 KB
Views:
57
2. Aug 30, 2015

Staff: Mentor

Welcome to the PF.

What's an MC?

3. Aug 30, 2015

TSny

Why do you say that n1 > n2? You might review your notes or textbook.

In order for total internal reflection to occur at the boundary between n1 and n2, does the angle of incidence θ (in your drawing) need to be greater than the critical angle or less than the critical angle?

What happens to the angle θ if the angle i is increased?

4. Aug 30, 2015

cainko

MC is multiple choice question:)

5. Aug 30, 2015

cainko

I am so sorry!!:( I draw the figure wrongly!
for t.i.r. light must travel from low speed to high sped,for light ray:larger n --> smaller n ==>n1>n2

θ will increase when angle i increased??
sini/sinr = n ; sini increase-->sinr decrease==>θ=90°-r, r decrease θ increase?
thx so much!

Attached Files:

• tir.png
File size:
1.5 KB
Views:
46
6. Aug 30, 2015

TSny

OK, no problem.
sin(i)/sin(r) = n implies that sin(i) = n sin(r). So, if sin(i) increases what happens to sin(r)?

7. Aug 30, 2015

cainko

decreases?

8. Aug 30, 2015

TSny

The equation sin(i) = n sin(r) says that sin(i) and sin(r) are directly proportional to one another. If one increases so does the other.

9. Aug 31, 2015

cainko

Oh, so r<90°-c ---> i is also<90°-c ?? so i is less than certain value?

10. Aug 31, 2015

TSny

No. You are right that the condition r < 90 - c will produce total internal reflection at X.
But that doesn't imply that the angle i must also be less than 90 - c. You are very close to the answer.

Let rc = 90 - c. So, when r = rc, θ = c. You correctly stated that whenever r is less than rc, you will get total internal reflection at X.

When r = rc, the angle i will have some value which we can call ic. How could you find ic if you knew rc? Does ic equal rc?

What is the condition on angle i such that you get total internal reflection at X?

11. Sep 4, 2015

cainko

as i increase when r increase, to make r< rc , i should be<ic too?

12. Sep 4, 2015

TSny

Yes.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted