Question 21

[jnguyen07080]

We want to find distance L in the diagram below.
From the previous question, sin icrit = ncladding / ncore
= 1.2 / 1.5
= 0.8
Notice now that we have a triangle with length of sides in the ratio 3:4:5, with the width of the fiber being the shortest side and L being the next
shortest.
Thus, L = (4/3) x 1 mm = 1.33 mm

How do we know that we have a 3:4:% triangle? I'm confused with the explanation to this question.

[admin]

As long as you see how to calculate the critical angle at 0.8 then the rest is straightforward:

0.8 = 4/5 = opposite/hypotenuse (because it is the sine function)

Because we have a right angle triangle, we can use the Pythagorean theorem to determine the ratio of all 3 sides given any 2 sides (which we have):

a^2 + b^2 = c^2 where c is the hypotenuse

Now we know the ratio of the sides must be 3:4:5

I hope that helps you.

[niv]

Could you please further explain this question? I understand the first part but not where L = (4/3) x 1 mm = 1.33 mm comes from.
Thank you.

[JoonSKim1557]

Oh, I get it. This question made me think for awhile. But make sure know that the angle you are projecting is from upper right corner of the triangle as drawn in the explanation. Then try to to figure it out. Though I don't think this complexity of question would be on MCAT, I hope...

[JoonSKim1557]

It seems to me though, I can't intuitively convince of myself, other than the equation makes sense to me. Does this mean that the light absorbing material (ie. lens) needs to have minimum thickness to cause internal reflection?

[quadalpha]

Ah, I admit I have no idea what this question is talking about. What does light absorbing material have to do with the angles? Where did the diagram in the explanation come from?

[jellywing_2058]

Basically, light is refracted as it passes from the cladding to the core. We don't want the light to get refracted back into the cladding, so it needs to "hit" the other side of the core with the critical angle. We are looking for the minimal horizontal distance traveled through the core (L) to get the critical angle. This can be found using:

sin (critical angle)= n(cladding)/(n(core)
sin (critical angle)= 1.2/1.5= 0.8
critical angle= sin-1[0.8]= 53 degrees

Tan 53= L/thickness or core
Tan 53= L/1mm
L= 1.33 mm