Question

A fiber optic cable (nfiber =1.47) is submerged in water (nwater =1.34). What is the critical angle for light to stay inside the cable?

Answer 1

The critical angle for light to stay inside the cable would be 41.1°.

Step-by-step explanation:

We can solve this using Snell's law and the critical angle condition.

Snell's law states: n1sin(θ1) = n2sin(θ2)

Where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the incident and refracted angles.

The critical angle (θc) is the angle at which the refracted ray travels along the interface between the two media (θ2 = 90°). At this angle, all light is totally internally reflected.

Substituting θ2 = 90° in Snell's law gives: sin(θc) = n2/n1

So in this case, with:

⇒ n1 = 1.47 (fiber optic cable)

⇒ n2 = 1.34 (water)

We have:

⇒ sin(θc) = 1.34/1.47

⇒ θc = sin-1(0.91) = 41.1°

Therefore, the critical angle for light to stay inside the fiber optic cable submerged in water is 41.1°.

At angles greater than 41.1°, total internal reflection will occur and the light will remain inside the cable.

Answer 2

65.72

Step-by-step explanation:

sin^-1(1.34/1.47)=65.72

see attached picture

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