A light ray entering an optical fiber (made from crown glass) surrounded by air

Question

A light ray entering an optical fiber (made from crown glass) surrounded by air is first refracted and then reflected as shown below. n n2 a. What is the minimum angle (greater than or equal to 0) at which an incident ray will still be totally internally reflected? Minimum angle ,- deg. (Only enter values 0 or greater.) b. What is the maximum angle (smaller than 90 deg) at which an incident ray will still be totally internally reflected? Maximum angle 1-1 deg. 1 c. If the optical fiber is made with material other than crown glass, what minimum value n2 is needed for refractive index of the material to ensure that all incident rays are totally internally reflected? kMinimum n2 needed

Explanation / Answer

A) minimum theta1 = 0 degree.

Because in this case theta2 will also be zero and theta3 will be 90 degree, So TIR will take place.

B) Maximum theta1 = 90 degree.

It is because, in this case, theta2 = arcsin( n1/n2) = arcsin (1/1.517)

= 41.24 degree which is also the critical angle for TIR.

theta3= 90-41.24 = 48.76 degree which is more than critical angle of 41.24 degree so TIR will take place.

C) In limiting case, for maximum theta1,

If theta2 is 45 degree, theta3 will also be 45 degree. And hence TIR will take place.

Minimum n2 = n1/sin 45 degree = sqrt 2

= 1.41 answer

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