Simple Fiber Optics Question. A symmetrical dielectric slab waveguide has n1=1.5

Question

Simple Fiber Optics Question.

A symmetrical dielectric slab waveguide has n1=1.5 and n2=1.48.

For the TE0 Mode compute d/lamda if the propagating angle is 86 degrees?

I have done the following:

neff=n1 Sin (theta) = 1.5 Sin(86) = 1.496

tan(hd/2)= (1/(1.5 Cos 86))(Sqrt((1.5 - Sin (86))^2 -(1.48^2)) = 2.11

tan(hd/2)= 2.11

HERE IS WHERE I NEED HELP!!! Converting this into hd/2 = 1.132 radians..... I am not sure how to do this in my calculator. I have switch my settings from degrees to radians and that does not give me the correct answer. Please help.

Explanation / Answer

As per your equation, the equation is in degrees. So

Tan(hd/2)=2.11

(hd/2) =tan-1(2.11). // Tan-1 == tan (inverse)

hd/2 is in degrees

hd/2=64.64 deg. (or) 1.13 rad

No matter whichever way your calculator functions. Please follow the following conversion

180 degrees = 3.14 radians

So 64.64 deg = (3.14/180)*64.64 = 1.13 rad

Similarly

1.13 rad = (180/3.14)*1.13 = 64.66 degrees

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