MC (multiple choice) question about total internal reflection

[cainko]

Homework Statement

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 canceled 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.

Homework Equations

sinθa/sinθg=1/n; sinc=1/n;n1/n2=v1/v2

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)

 

[berkeman]

Welcome to the PF.

What's an MC?

 

[TSny]

(I have canceled 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.

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

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?

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?

 

[cainko]

Welcome to the PF.

What's an MC?

MC is multiple choice question:)

 

[cainko]

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?

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!

 

[TSny]

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

OK, no problem.

sini/sinr = n ; sini increase-->sinr decrease

sin(i)/sin(r) = n implies that sin(i) = n sin(r). So, if sin(i) increases what happens to sin(r)?

 

[cainko]

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)?

decreases?

 

[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.

 

[cainko]

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.

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

 

[TSny]

Oh, so r<90°-c ---> i is also<90°-c ??

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

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

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

 

[cainko]

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

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

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

as i increase when r increase, to make r< r_c , i should be<i_c too?

 

[TSny]

as i increase when r increase, to make r< r_c , i should be<i_c too?

Yes.