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.
a) The photon and its properties. A photon is the quantum (discrete packet) of electromagnetic energy — light interacts with matter not as a continuous wave but in indivisible units. Its key properties: energy $E=h\nu=hc/\lambda$ (set by frequency alone); momentum $p=E/c=h/\lambda$; it is massless and travels at $c$ in vacuum; it carries one unit of spin angular momentum (spin‑1, giving rise to the two circular polarization states); and it is its own antiparticle. A photon is either absorbed or emitted as a whole quantum — there is no such thing as "half a photon" being absorbed.
b) Energy of a 0.5 μm photon.
Given. $\lambda=0.5\ \mu\text{m}=5\times10^{-7}\ \text{m}$; $h=6.626\times10^{-34}\ \text{J}\cdot\text{s}$ (CODATA value; see check note above); $c=3\times10^8$ m/s.
Find. $E=hc/\lambda$.
c) Optical process removing the 0.5 μm photons. The gas atoms have discrete, quantized electronic energy levels. Any photon whose energy $h\nu$ exactly matches the energy gap between the atom’s ground state and an excited state can be absorbed, promoting an electron to that excited state; photons of other energies pass through largely unaffected because no matching transition exists. The re-emitted photon (as the excited atom relaxes) is emitted in a random direction, not preferentially back along the original beam axis, so a dark absorption line appears at 0.5 μm in the transmitted (forward) spectrum even though the energy is not destroyed — only redirected. This is the same physical process (resonant absorption between quantized atomic levels) that produces the Fraunhofer absorption lines in sunlight passed through the solar atmosphere.
d) Emission spectrum once the gas is heated and glows. A hot, glowing gas radiates by spontaneous emission as thermally-excited electrons fall back to lower energy states — by Kirchhoff’s law of thermal radiation, a gas emits (and absorbs) at exactly the same characteristic wavelengths, since both processes are governed by the same set of quantized energy-level spacings. The 0.5 μm line that was missing (dark) in the absorption spectrum now appears as a bright emission line against an otherwise dark background, together with the gas’s other characteristic emission lines elsewhere in the visible range.
