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Define na and derive the relation between na and relative refractive index.

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Question: Derive the expression of Numerical Aperture of Step- index fiber. What will happen to Numerical Aperture if cladding is removed?

Mumbai University > Electronics and Telecommunication > Sem7 > Optical Communication and Networks

Marks: 5M

Year: May2014, Dec2013, Dec2012

mumbai universityoptical communication and networks• 6.9k views

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modified 21 months ago  •written 21 months ago by Ramnath • 2.8k

Numerical Aperture is the ability of fiber to collect the light from the source and save the light inside it by maintaining the condition of total internal reflection.

Consider a light ray entering from a medium air of refractive index no" role="presentation" style="box-sizing: border-box; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">nono into the fiber with a core of refractive index n1" role="presentation" style="box-sizing: border-box; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">n1n1which is slightly greater than that of the cladding n2" role="presentation" style="box-sizing: border-box; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">n2n2.

Applying Snell’s law of reflection at point A,

sin⁡Ө1sin⁡Ө2=n1no=n1  as  n0=1" role="presentation" style="box-sizing: border-box; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">sinӨ1sinӨ2=n1no=n1  as  n0=1sin⁡Ө1sin⁡Ө2=n1no=n1  as  n0=1

In right angled Δabc,

θ2=π2−∅c" role="presentation" style="box-sizing: border-box; display: inline; font-style: normal; font-weight: normal; line-height: normal; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">θ2=π2−∅cθ2=π2−∅c

sinθ1=n1sin(π2−∅c)=n1cos∅c" role="presentation" style="box-sizing: border-box;