Does the NA of a Fibre Change When Immersed in Water?

[Cydrus]

1. What will the NA of the fibre be if it's immersed in water?
Basically we know the NA = 0.30 and refractive index is 1.50 for the fibre's core.


2. Snell's law


3. My theory is that NA is the sine of the critical angle.
n1 = 1.5, n2 = 1.333
NA = sin (theta_crit) = sin (arcsin (n2/n1)) = n2/n1 = 0.89

But our teacher said it was not correct but on the right track. Is there a possibility that the NA doesn't even
change when the fibre is immersed in water?

 

[anathema]

Thank you for your question. I would like to provide some clarification on the concept of numerical aperture (NA) and its relation to the refractive index and immersion in water.

Firstly, numerical aperture is defined as the measure of the acceptance angle of a fiber, which is determined by the refractive index of the core and the surrounding medium. In this case, the NA of the fiber (NA_fiber) is 0.30, which means that the fiber can accept light at an angle up to 18 degrees from the fiber axis.

Secondly, when a fiber is immersed in a medium with a different refractive index, the effective NA (NA_eff) changes. This is because the light rays entering the fiber are now refracted at a different angle due to the change in refractive index of the surrounding medium. The formula for calculating NA_eff is NA_eff = n1sin(theta_crit), where n1 is the refractive index of the core and theta_crit is the critical angle at which total internal reflection occurs.

Based on this formula, your calculation for NA_eff is correct. However, it is important to note that the refractive index of water (n2=1.333) is lower than the refractive index of the fiber core (n1=1.50). This means that the critical angle (theta_crit) will also change, resulting in a different NA_eff value.

In conclusion, the NA of the fiber will change when it is immersed in water, but the exact value will depend on the refractive index of the water and the fiber core. It is possible that the NA may not change significantly, but it will not remain the same. I hope this helps clarify your understanding of the concept.