Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index $$n1$$ surrounded by a medium of lower refractive index $$n2$$. The light guidance in the structure takes place due to successive total internal reflections at the interface of the media $$n1$$ and $$n2$$ as shown in the figure. All rays with the angle of incidence i less than a particular value im are confined in the medium of refractive index $$n1$$. The numerical aperture (NA) of the structure is defined as sinim.For two structures namely $$S1$$ with $$n1=45/4$$ and $$n2=3/2$$, and $$S2$$ with $$n1=8/5$$ and $$n2=7/5$$ and taking the refractive index of water to be $$4/3$$ and that of air to be $$1$$, the correct $$option(s)$$ is $$(are)If$$ two structures of same $$cross-sectional$$ area, but different numerical apertures $$NA1$$ and $$NA2NA2$$

Question

Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index  $$n1$$ surrounded by a medium of lower refractive index $$n2$$.  The light guidance in the structure takes place due to successive total internal reflections at the interface of the media $$n1$$  and  $$n2$$ as shown in the figure.  All rays with the angle of incidence i  less than a particular value im  are confined in the medium of refractive index  $$n1$$.  The numerical aperture (NA) of the structure is defined as sinim.For two structures namely  $$S1$$ with  $$n1=45/4$$ and  $$n2=3/2$$, and $$S2$$  with $$n1=8/5$$  and  $$n2=7/5$$ and taking the refractive index of water to be  $$4/3$$ and that of air to be $$1$$, the correct $$option(s)$$ is $$(are)If$$ two structures of same $$cross-sectional$$ area, but different numerical apertures  $$NA1$$ and  $$NA2NA2$$

Infinity Learn · Accepted Answer

$$A)$$ For critical angle of $$S1$$ , $$sin$$θ$$=n2n1=32454=645$$∴$$sin90-$$θ$$=345Snell$$'s Law , $$43sin$$⁡$$i=454sin$$⁡(90$$−θ$$)⇒$$43sin$$⁡$$i=454345$$⇒$$sin$$⁡$$i=916=NA$$  For critical angle of $$S2$$ , $$sin$$θ$$=n2n1=7585=78$$∴$$sin90-$$θ$$=158Snell$$'s Law , $$16315sin$$⁡$$i=85sin$$⁡(90$$−θ$$)⇒$$2315sin$$⁡$$i=15158$$⇒$$sin$$⁡$$i=3$$×$$1580=916=NAA$$ is correct $$B)$$ Snell's Law for $$S1$$ , $$615sin$$⁡$$i=454sin$$⁡(90$$−θ$$)⇒$$615sin$$⁡$$i=454345$$⇒$$sin$$⁡$$i=31524Snell$$'s Law for $$S2$$ ,$$43sin$$⁡$$i=85sin$$⁡(90$$−θ$$)⇒$$43sin$$⁡$$i=85158$$⇒$$sin$$⁡$$i=31520B$$ is wrong  $$C)$$ Snell's Law for $$S1$$ , $$1sin$$⁡$$i=454sin$$⁡(90$$−θ$$)⇒$$1sin$$⁡$$i=454345$$⇒$$sin$$⁡$$i=34Snell$$'s Law for $$S2$$ ,$$415sin$$⁡$$i=85sin$$⁡(90$$−θ$$)⇒$$415sin$$⁡$$i=85158$$⇒$$sin$$⁡$$i=34C$$ is correct  $$D)$$ Snell's Law for $$S1$$ , $$1sin$$⁡$$i=454sin$$⁡(90$$−θ$$)⇒$$1sin$$⁡$$i=454345$$⇒$$sin$$⁡$$i=34Snell$$'s Law for $$S2$$ ,$$43sin$$⁡$$i=85sin$$⁡(90$$−θ$$)⇒$$43sin$$⁡$$i=85158$$⇒$$sin$$⁡$$i=31520D$$ is wrong Smaller one in the given two values must be NA for system. Hence $$NA2$$ is the numerical aperture of the combined structure.

Best Courses for You

Detailed Solution

courses

Get Expert Academic Guidance – Connect with a Counselor Today!

best study material, now at your finger tips!

download the app

Download the App