Category: Part 5: Optics

Problem Statement Solve the quantum/modern physics problem: A photodetector receives $N = 10^6$ photons per second at $\lambda = 500$ nm. Find (a) the photocurrent for quantum efficiency $\eta = 0.8$, (b) the shot noise current (RMS) in a bandwidth $\Delta f = 1$ Hz. (a) Photocurrent: $I = \eta N e = 0.8\times10^6\times1.6\times10^{-19} =…

Problem Statement In an HBT experiment, two detectors are placed symmetrically. For thermal light, the intensity correlation $g^{(2)}(0) = 2$, while for coherent (laser) light $g^{(2)}(0) = 1$. Explain the physical meaning. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts &…

Problem Statement Solve the oscillation/wave problem: An echelle spectrograph uses cross-dispersion to separate overlapping orders. The echelle operates in orders $m = 50$–$80$ for $\lambda = 400$–$700$ nm. Find the wavelength range in order $m = 60$. For a given order $m$, wavelength range within one FSR: $$\Delta\lambda = \lambda/m = 550/60 \approx 9 Given…

Problem Statement Solve the optics problem: In OCT, a broadband source with $\Delta\lambda = 50$ nm centered at $\lambda_0 = 830$ nm is used. Find the axial resolution (coherence length in tissue, $n = 1.38$). Axial resolution in OCT: $$\delta z = \frac{2\ln 2}{\pi}\frac{\lambda_0^2}{n\Delta\lambda} = \frac{0.441\times(830)^2}{1.38\times50}\t Given Information Refractive index $n$ or focal length $f$…

Problem Statement Solve the optics problem: A spherical glass ball of radius $R = 5$ cm and $n = 1.5$ acts as a burning glass. Find the focal point for parallel incident rays. Using refraction at two spherical surfaces (Problem 5.25 method) for parallel rays ($u = \infty$): Surface 1 (air to glass, $R_1 =…

Problem Statement Solve the optics problem: Find the cardinal points (focal points, principal planes, nodal points) for a thick lens of glass ($n = 1.5$) with radii $R_1 = 20$ cm, $R_2 = -20$ cm, thickness $t = 5$ cm. Using matrix optics (system matrix $M = M_{exit}\cdot M_{prop}\cdot M_{entry}$): $M_{entry} = \begin{pmatrix}1 0\\-P_1 1\end{p…

Problem Statement Represent the following polarization states on the Poincaré sphere: (a) horizontal linear, (b) vertical linear, (c) +45° linear, (d) left circular. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The…

Problem Statement Solve the optics problem: A laser pulse of peak intensity $I_0 = 10^{13}$ W/m² travels through glass ($n_2 = 3\times10^{-20}$ m²/W, $L = 10$ mm). Find the maximum nonlinear phase shift. Nonlinear phase shift (B-integral): $$\phi_{NL} = \frac{2\pi}{\lambda}n_2 I_0 L = \frac{2\pi}{1000\times10^{-9}}\times3\times10^{-20}\times1 Given Information Refractive index $n$ or focal length $f$ as given…

Problem Statement Solve the work-energy problem: Explain the difference between chromatic resolving power $\mathcal{R}_c = \lambda/\delta\lambda$ and spatial resolving power $\mathcal{R}_s = 1/\delta x$ of an optical instrument, giving examples of each. Chromatic resolving power $\mathcal{R}_c = \lambda/\delta\lambda$ measures ability to distingui Given Information Mass $m$, velocity $v$, height $h$, or other given quantities Any…

Problem Statement In Young’s experiment with slit width $b = 0.1$ mm and separation $d = 0.5$ mm, $\lambda = 500$ nm, $L = 1.0$ m. Find where the double-slit fringes are missing due to single-slit minima. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see…