1. A microscope has an objective with f = 1 cm, an ocular with f = 2.5 cm, and a distance s = 10 cm between them. Taking the best viewing distance as 25 cm,
a) Find the magnification of a microscope
b) Plot the picture of the rays to scale using the graph paper.
2. Model a parabolic graded-index fibre with n(r) = n1[1 - (r / a)2 Δ] for r ≤ a , with n1 = 1.5 , a = 0.1 mm and Δ = 0.01, by the equivalent multiple-step approximation. Divide the radius into 10 equal parts. Consider a ray inside the fibre crossing the fibre axis at 5o with respect to that axis. Using the graph paper, plot the progress of the ray through the fibre until it turns back and re-crosses the fibre axis. (Angles can be magnified on the plot.) At what value of r / a will the ray turn back? Does it depend on the value of a ?
3. In a step-index fibre, the refraction coefficients of the core and the cladding layer are 1.505 and 1.500, respectively.
a) Find the radius of the core, at which the fibre would perform as a single-mode at the wavelength of 1.3 μm, using a typical design criterion of V = 2 .
b) Find the cut-off wavelength for this fibre.
c) If the refractive index of the core was not 1.505 but 1.504, which cut-off wavelength (larger or smaller) would you expect?
Provide explanations.
(Note that a version of this problem in the handouts is incorrect. The correct version is above.)
4. Explain in your own words the difference between photoluminescence and electroluminescence.
5. Explain, why an LED operating at the fixed current would be more stable than that operating at the fixed voltage. Consider the effect of the device heating on the I(V) characteristics. Explain under which condition there would be positive or negative feedback from the heating.
6. A laser diode has a threshold current of 10 mA and a slope of its optical power versus input current of 2 mW/mA. The diode current is I = A + B sinω t . Plot the output power as a function of time if:
a) A=20 mA; B=2 mA;
b) A=10 mA; B=2 mA.
7. A p-n photodiode acts as a photocell, the circuit is shown in the handouts. Outline the band profile of the diode for infinitely large RL for different levels of illumination.