Category: Part 5: Optics

Problem Statement Solve the oscillation/wave problem: A rectangular aperture ($a = 0.5$ mm wide, $b = 1.0$ mm tall) is illuminated by a plane wave ($\lambda = 500$ nm). A lens ($f = 1.0$ m) focuses the diffraction pattern. Find the dimensions of the central maximum. The central maximum extends to the first minima in…

Problem Statement A laser beam ($\lambda = 633$ nm) illuminates a rough surface of diameter $D = 20$ mm. A screen is placed $L = 1.0$ m away. Estimate the average speckle size. 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 quantum/modern physics problem: Solve the quantum/modern physics problem: A 1D photonic crystal has alternating layers of $n_1 = 1.5$ (thickness $d_1 = 100$ nm) and $n_2 = 1.0$ (thickness $d_2 = 150$ nm). Estimate the centre wavelength of the first stop band at normal incidence. For a quarter-wave stack condition: $n_1…

Problem Statement A Fabry-Perot etalon ($d = 5$ mm, $n = 1.5$, $R = 0.95$) is used to analyse the spectrum near $\lambda = 500$ nm. Find the free spectral range, finesse, and minimum resolvable linewidth. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles…

Problem Statement Write the Mueller matrix for an ideal linear polarizer with transmission axis at $\theta = 0°$ (horizontal), and find the Stokes vector of the output when the input is $(S_0, S_1, S_2, S_3) = (1, 0, 0, 0)$ (unpolarized). Given Information See problem statement for all given quantities. Physical Concepts & Formulas This…

Problem Statement The Rayleigh scattering cross section of an air molecule at $\lambda = 500$ nm is approximately $\sigma = 5\times10^{-31}$ m². The number density of air at STP is $n = 2.69\times10^{25}$ m$^{-3}$. Find the scattering mean free path. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem…

Problem Statement Blue light ($\lambda_B = 450$ nm) and red light ($\lambda_R = 650$ nm) pass through an atmosphere of optical depth $\tau_B$ and $\tau_R$. Using $\tau \propto \lambda^{-4}$, find the ratio of transmitted intensities $I_B/I_R$ if $\tau_R = 0.10$ at zenith and the path is at zenith angle $z = 60°$. Given Information See…

Problem Statement An echelle grating (300 lines/mm, blaze angle $\gamma = 63°$) is used near order $m = 50$ for $\lambda = 500$ nm. Find the angular dispersion and resolving power (grating width $W = 100$ mm). Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics…

Problem Statement A slit of width $a = 0.3$ mm is illuminated by a mercury lamp filtered to $\lambda = 546$ nm. A lens of focal length $f = 60$ cm focuses the Fraunhofer pattern. Find the full width of the central maximum and the positions of the first secondary maxima. Given Information See problem…

Problem Statement The photopic luminous efficiency function peaks at $\lambda = 555$ nm with $V(555) = 1.0$ and has $V(450) = 0.038$, $V(650) = 0.107$. A lamp emits equal radiant flux at all three wavelengths. Find the relative luminous fluxes. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem…