CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Lens Maker's Formula

Light guidanc...

Question

Light guidance in an optical fibre can be understood by considering a structure comprising of thin solid glass cylinder of refractive index $n_{1}$ surrounded by a medium of lower refractive index $n_{2}$ .
The light guidance in the structure takes place due to successive total internal reflections at the interface of the media $n_{1}$ and $n_{2}$ as shown in the figure. All rays with the angle of incidence $i$ less than a particular value $i_{m}$ are confined in the medium of refractive index $n_{1}$ . The numerical aperture (NA) of the structure is defined as $sin i_{m}$ .

If two structures of same cross-sectional area, but different numerical apertures NA $_{1}$ and $N A_{2} (N A_{2} < N A_{1})$ are joined longitudinally, the numerical aperture of the combined structure is

A

\frac{N A_{1} N A_{2}}{N A_{1} + N_{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

N A_{1} + N A_{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

N A_{1}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

N A_{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $N A_{2}$
$N A_{2} < N A_{1}$

$\Rightarrow i_{m 2} < i_{m 1}$

If the combination is placed in any order, Total internal Reflection if satisfied for lower $i_{m}$ , it can be satisfied for any lower angles as well.

$∴$ $N A_{2}$ will be the numerical aperture of the combined structure.

Suggest Corrections

thumbs-up

5

Similar questions

Q. Light guidance in an optical fibre can be understood by considering a structure comprising of thin solid glass cylinder of refractive index

n_{1}

surrounded by a medium of lower refractive index

n_{2}

.
The light guidance in the structure takes place due to successive total internal reflections at the interface of the media

n_{1}

n_{2}

as shown in the figure. All rays with the angle of incidence

i

less than a particular value

i_{m}

are confined in the medium of refractive index

n_{1}

. The numerical aperture (NA) of the structure is defined as

sin i_{m}

.

If two structures of same cross-sectional area, but different numerical apertures NA

_{1}

N A_{2} (N A_{2} < N A_{1})

are joined longitudinally, the numerical aperture of the combined structure is

Q. Light guidance in an optical fibre can be understood by considering a structure comprising of thin solid glass cylinder of refractive index

n_{1}

surrounded by a medium of lower refractive index

n_{2}

.
The light guidance in the structure takes place due to successive total internal reflections at the interface of the media

n_{1}

n_{2}

as shown in the figure. All rays with the angle of incidence

i

less than a particular value

i_{m}

are confined in the medium of refractive index

n_{1}

. The numerical aperture (NA) of the structure is defined as

sin i_{m}

For two structures namely

S_{1}

n_{1} = \sqrt{45} / 4

n_{2} = 3 / 2

S_{2}

n_{1} = 8 / 5

n_{2} = 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)

Q. If two structure of same cross-sectional area, but different numerical apertures

N A_{1}

N A_{2} (N A_{2} < N A_{1})

are joined longitudinally, the numerical aperture of the combined structure is

Q. A light ray moving in medium - I (of refractive index

n_{1}

) is incident on interface of two media and it is totally internally reflected at the interface. Now, refractive index

n_{2}

of medium - II is decreased, then:

Q. Acceptance angle

(θ)

for an optical fiber is defined as the maximum angle of incidence at the interface of medium (air usually) and core

(μ = n_{1})

for which light ray enters and travel along the optical fiber. Sine of acceptance angle is known as numerical aperture of the optical fiber. Then in the given setup, what is the value of numerical aperture?

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Thin Lenses: Point Objects

PHYSICS

Watch in App

explore_more_icon

Explore more

Lens Maker's Formula

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon