Answer to Question #142890 in Optics for pranta

Question

. Skew rays are accepted into a large core diameter compared to the wavelength of thetransmitted light) step index fiber in air at a maximum axial angle of 450. Within the fiberthey change direction by 900at each reflection. Determine the acceptance angle formeridional rays or the fiber in air

Answer 1

Given,

Axial angle $(\theta_{as}) =45^\circ$

As per the question, skew changes the direction by $90^\circ$ at each reflection,

hence, $\gamma=45^\circ$

$\theta_{as}=\sin^{-1}(\frac{NA}{\cos\gamma})$

$\Rightarrow NA= \sin(\theta_{as})\times \cos(\gamma)$

$\Rightarrow NA = \sin(45)\times \cos(45^\circ)$

$\Rightarrow NA =\frac{1}{2}$

Now, Acceptance angle for meridional rays $\theta_{a}=\sin^{-1}(NA)$

$\Rightarrow \theta_{a}=\sin^{-1}(0.5)$

$\Rightarrow \theta_{a}=30^\circ$