17-Phys-A7 Optics · Undated paper
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
17-Phys-A7, Optics — National Exams, May 2019. 3 hours; closed book (approved Casio/Sharp calculator only). Each question value is as indicated; exam is out of 67. Questions 1–6 are mandatory; the paper then offers a choice of Question 7 or 8, and a choice of Question 9 or 10. Every question is solved in full below as a complete study resource, including both members of each either/or pair.
Reference texts. Hecht, Optics, 5th ed.; Pedrotti, Pedrotti & Pedrotti, Introduction to Optics, 3rd ed.; Griffiths, Introduction to Electrodynamics, 4th ed. (Ch. 7–9, Maxwell’s equations and EM waves).
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
Detector selected: the PIN photodiode.
a) Physical structure. A PIN photodiode is a semiconductor photodetector built as three layers: a thin, heavily-doped p⁺ layer at the illuminated surface, a thick, lightly-doped (nominally undoped) intrinsic (i) layer in the middle, and a heavily-doped n⁺ substrate at the back, with ohmic metal contacts on the outer p⁺ and n⁺ faces. The device is operated under reverse bias, which extends the depletion region to fill essentially the entire intrinsic layer, producing a strong, uniform electric field across it. The thick intrinsic region (compared with a simple p-n photodiode) is the device’s defining feature: it gives incoming photons a long absorption path (high quantum efficiency) while keeping the depletion capacitance low and the transit time well-defined (high speed).
b) Optical processes in operation. An incident photon with energy $h\nu$ greater than the semiconductor’s bandgap $E_g$ is absorbed in the intrinsic region, promoting an electron from the valence band to the conduction band and leaving behind a hole — the internal photoelectric effect, creating an electron–hole pair. The strong electric field of the reverse-biased depletion region immediately sweeps the electron toward the n⁺ contact and the hole toward the p⁺ contact before they can recombine, producing an external photocurrent proportional to the incident optical power. No internal gain occurs (unlike an avalanche photodiode or photomultiplier) — each absorbed photon contributes at most one electron to the external circuit, so responsivity is set by quantum efficiency alone.
c) Applications. (i) Fiber-optic communication receivers — PIN photodiodes are the standard front-end detector converting the modulated optical signal from a fiber back into an electrical signal, valued for their linearity, speed, and low noise at moderate signal levels. (ii) Optical power meters and photometry — their linear response over a wide dynamic range makes them the detector of choice for calibrated laser/LED power measurement. (iii) General light-sensing and switching — proximity sensors, barcode scanners, and light-level sensing in consumer electronics, where their simplicity, low bias voltage, and room-temperature operation are advantageous compared with photomultipliers (which need high-voltage supplies) or avalanche photodiodes (which need careful bias control for stable gain).
