An optical fibre has numerical aperture (NA) of 0.3 and refractive index $\eta_2$ of cladding material is 1.6. What is the refractive index of core material?
1.63
To determine the refractive index of the core material, we will use the formula for the numerical aperture (NA) of an optical fibre, which is given by:
\(NA = \sqrt{n_1^2 - n_2^2}\)
where \(n_1\) is the refractive index of the core and \(n_2\) is the refractive index of the cladding.
We are given:
- Numerical Aperture, \(NA = 0.3\)
- Refractive index of the cladding, \(n_2 = 1.6\)
We need to find \(n_1\). Plugging the values into the formula:
\(0.3 = \sqrt{n_1^2 - (1.6)^2}\)
Squaring both sides, we get:
\(0.09 = n_1^2 - 2.56\)
Rearranging the equation to solve for \(n_1^2\):
\(n_1^2 = 0.09 + 2.56\)
\(n_1^2 = 2.65\)
Taking the square root of both sides to find \(n_1\):
\(n_1 = \sqrt{2.65}\)
\(n_1 \approx 1.63\)
Therefore, the refractive index of the core material \((n_1)\) is approximately 1.63.
The correct answer is 1.63.
Similar Questions
If numerical aperture and fractional refractive index of an optical fibre are 0.22 and 0.012, respectively. The refractive index of core (µ1) and cladding (µ2) will be
Which of the following is not a usual classification of optical fibre ?
Assertion (A) : In the propagation of light along multimode graded index fibre, the rays moving toward the cladding travel longer path with greater velocity than the rays travelling shorter path near the axis of fibres. These cause less spreading as compared to spreading caused by multimode step index fibre.
Reason (R) : The velocity varies because refractive index of the multimode graded index fibre increases with radial distance from the centre (axis).
Match the following lists :
List – I List – II a. \(\pi a\,NA/\lambda\) i. attenuation factor (dB/km) b. \(10\log_{10}\left(\dfrac{P_{in}}{P_{out}}\right)\) ii. Intermodal time delay c. \(\dfrac{l}{L}\dfrac{dt_g}{d\lambda}\) iii. Dispersion causing pulse spreading d. \(\dfrac{L(n_1-n_2)n_1}{n_2c}\) iv. Number of modes produced by an optical fibre Assertion (A) : Attenuation and dispersion have negative effects on the propagation of signal in the optical fibres.
Reason (R) : Optical signal degradation is caused due to structural imperfections of the fibre material.
Select your answer using the codes given below.
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