What is the range of the angles of the incident rays, Physics

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Q. Figure shows across

(b)What is the answer if there is no outer covering of the pipe?

556_What is the range of the angles of the incident rays.png

Answer

Reflection, rmax = 900-i=900-590=310    

Let, imax  be the (a) A Refractive index of the glass fibre μ=16.8

A Refractive index of the outer covering of the pipe ,μ =1.44

Angle of incidence = i

Angle of refraction = r

Angle of incidence at the interface = i'

The refractive index(6)of the inner core-outer core inter face is given as:

1833_What is the range of the angles of the incident rays1.png

For the critical angle, total internal reflection (TIR) takes place only when i>i' ,i. e., i >59°

Maximum angle of maximum angle  of incidence.

The refractive index at the air-glass interface μ1=1.68

We have the relation used for the maximum angles of incidence and reflection as:

2241_What is the range of the angles of the incident rays2.png

Thus, all the rays incident at angles lying in the range 0 < i< 60°will suffer total internal reflection.

(b)If the outer covering of the pipe is not present then:

Refractive index of the outer pipe,

For the angle of incidence i=90°,we can write Snell's law at the air-pipe interface as:

2066_What is the range of the angles of the incident rays3.png

While  i'> r all incident rays will suffer total internal reflection.


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