Below is a simple optical fiber surrounded by air, with no outer layer or coatin

Question

Below is a simple optical fiber surrounded by air, with no outer layer or coating. Red light is beamed straight down the fiber from the left. The fiber has a bend of angle "A".

A)If the index of refraction in the fiber is n=1.7, what is the largest angle "A" can be if no light is to escape the bend?

B)How would this angle "A" change if green light were used? EXPLAIN

PLEASE explain very clearly each step into solving this to help me understand, including any formulas. Full points for clear answers. Thanks

Explanation / Answer

a) First find the critical angle c.

    Use Snells Law [n1sin(1) = n2sin(2)] but becuase for no light to escape, we must get total internal refraction (in other words, the reflected beam must be at least 90 degrees from the surface.)

so the equation becomes:

n1sin(1) = n2sin(90)

[take the left side of the equation to be in the fiber and the right to be when the light exits into air]

We are trying to solve for 1, which is the crit angle, so rearrange the eq to become:

1 = arcsin(n2 / n1)       

or 1 = arcsin(1.0 / 1.7) = 36.03 degrees.

Because of how the critical angle is related to the bend (turning the figure around so that the part after the bend is horizontal and the beam is hitting that part at an angle may make it easier to see) the largest angle will be:

90 - 36.03 = 53.97 degrees.

b) Nothing will change, as the speed of light is the same for all light regardless of color, and only the frequency will change. Change in frequency does not affect the refractive index.

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