How Is the Minimum Bend Radius of a Fiber Optic Cable Determined?

[doggydan42]

If there is a fiber optic cable with a diameter d, the index of refraction of the cladding the cable is given, and so is the index of refraction core of the cable, how would you formulate an equation for the minimum radius of bend the cable can have?

Thank you in advance.

 

[sophiecentaur]

What is it that determines whether a ray will be internally reflected or not? How could that idea be applied to a curved surface? Try some sketch diagrams of rays and curves.

 

[doggydan42]

What is it that determines whether a ray will be internally reflected or not? How could that idea be applied to a curved surface? Try some sketch diagrams of rays and curves.

For internal reflection, I tried to find the critical angle, which would be:

$$\theta_c = sin^{-1}(\frac{n_{cladding}}{n_{core}})$$

However, I was confused about how this would be applied to the curved surface. Is there a specific equation for that?

Thank you.

 

[lekh2003]

For internal reflection, I tried to find the critical angle, which would be:

$$\theta_c = sin^{-1}(\frac{n_{cladding}}{n_{core}})$$

However, I was confused about how this would be applied to the curved surface. Is there a specific equation for that?

Thank you.

It would be essentially the same for a curved surface. A curved surface is simply a combination of several flat surfaces.

 

[doggydan42]

It would be essentially the same for a curved surface. A curved surface is simply a combination of several flat surfaces.

That makes sense but how do I relate the critical angle to the radius of the surface?

 

[Andy Resnick]

That makes sense but how do I relate the critical angle to the radius of the surface?

This is a problem of geometry, specifically chords. My hint is that you need to find how the angle of incidence changes when the ray path becomes a chord of a circle with radius 'r'