Category: Part 5: Optics

Problem Statement Solve the oscillation/wave problem: In Young’s experiment, the source has spatial coherence function $\gamma_{12}$. The two slits are separated by $d = 0.5$ mm. The source (width $b = 0.1$ mm) is at distance $R = 1.0$ m. Find the visibility of fringes at $\lambda = 500$ nm. Spatial coherence between the slits…

Problem Statement Solve the optics problem: An optical isolator uses a Faraday rotator (45°) between two polarizers at 45° to each other. Explain why forward light passes but backward-traveling light is blocked. Forward path : Light polarized at $0°$ by Polarizer 1, rotated $+45°$ by Faraday rotator, passes through Polarizer 2 (at $45°$). Tra Given…

Problem Statement The power spectral density of a source is Lorentzian: $S(\nu) = S_0/(1+(2\pi(\nu-\nu_0)\tau_c)^2)$. Find the autocorrelation function (coherence function) and coherence time. 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 oscillation/wave problem: A high-reflectance mirror consists of alternating layers $(HL)^5 H$ where H is TiO$_2$ ($n_H = 2.35$) and L is SiO$_2$ ($n_L = 1.45$), each $\lambda/4$ thick. Estimate the peak reflectance near $\lambda = 500$ nm. For a quarter-wave stack on glass ($n_g = 1.5$) and air ($n_0 = 1$),…

Problem Statement Solve the optics problem: State the Huygens-Fresnel principle and use it to derive qualitatively why a plane wave remains a plane wave after passing through a large aperture (no diffraction in that limit). Huygens-Fresnel principle : Every point on a wavefront acts as a source of secondary spherical wavelets. The amplitude a Given…

Problem Statement Design an anti-reflection coating for a camera lens (glass $n_g = 1.72$) to minimize reflection at $\lambda = 550$ nm. Find the required film index and thickness. Available materials: MgF$_2$ ($n = 1.38$) and ZrO$_2$ ($n = 2.10$). Given Information All quantities, constants, and constraints stated in the problem above Physical constants used…

Problem Statement Solve the oscillation/wave problem: A grating spectrometer is used to study $\lambda = 400$ nm light in 3rd order. What wavelengths of 2nd order radiation overlap with this measurement, and how can they be filtered out? Overlapping occurs when $m_1\lambda_1 = m_2\lambda_2$: $3\times400 = 2\lambda_2 \implies \lambda_2 = 600$ nm. Also: Given Information…

Problem Statement Solve the optics problem: A glass prism ($n_D = 1.60$, $dn/d\lambda = -800$ m$^{-1}$ at $D$ line) has base $b = 40$ mm and refracting angle $\Theta = 60°$. Find the angular dispersion $d\theta/d\lambda$ at minimum deviation. At minimum deviation, the deviation angle $\delta_m$ satisfies $\sin(\Theta/2) = n\sin(r)$ with $r = Given Information…

Problem Statement Solve the work-energy problem: An echelon grating has 20 glass plates each of thickness $t = 5$ mm ($n = 1.5$) stacked with step $s = 1$ mm. Find the resolving power near $\lambda = 500$ nm in 1st order. Path difference between adjacent plates: $\Delta = (n-1)t + s$ (glass path minus…

Problem Statement Near an absorption resonance, glass shows anomalous dispersion. Explain what anomalous dispersion means and where $dn/d\lambda > 0$ implies about pulse propagation. 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.…