# Determination of Numerical Aperture and the energy loss related to Optical fiber

THEORY:

Numerical Aperture: The Numerical Aperture (N.A.) of a system is the measure of  the light collected by that optical system.

N.A. of a system = μsinθ

For air μ = 1

Therefore, N.A. = sinθ

Apparatus:

Fiber optic analog transmission kit, Fiber optic analog receiver kit, one meter PMMA fiber cord, five meter PMMA fiber cord, inline SMA adaptor.

Procedure:

1. In a dark room connect the 1 m optical fiber with the LED port of the device from which light may enter the fiber. Insert the other end of the fiber through the hole of the L-shaped numerical aperture measurement kit. Place the calibrated screen plate vertically on the mark (L) of the scale of the L-shaped kit. Switch on the machine. Make a bright circle on the vertical plate by adjusting the intensity knob. Note down the value of L. Adjust the vertical plate so that the bright circle is symmetrical with respect to scales drawn on it. Measure the value of the diameter of the circle (W).
2. Move the vertical screen to several other values of L. Note down the value of W in each case.
3. Take out the output end of the fiber and connect it to the power measuring port. Apply an input voltage by the turning the set P0 knob. Make sure that the cable is fully stretched without any coiling or bending. Measure the input voltage and the output power with the help of a voltmeter/multimeter. Repeat this step several times by changing the input voltage. These are the values of P01.
4. Repeat step 3 for the longer cable. You should measure the power for the same setting of input voltage. These are P02.
5. Repeat step 3 but this time joining the two cables by inline SMA. These are the values of P03.

Experimental Results:

1. Determination of Numerical aperture:
 No. of Obs. L (mm.) W (mm.) N.A. = W/(4L2+W2) Mean N.A.

1. Determination of Energy loss:
 No. of Obs. Input Voltage (mV) P01 in dBm P02 in dBm P03 in dBm Loss in C1 and A (P03-P02) dB Loss in C2 and A (P03-P01) dB Loss per meter (dBm) Loss due to adaptor (dB)

Calculation:

Average loss per meter in fibre optics =

Average loss due to SMA =

Percentage error:

Conclusion:

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