Category: Part 5: Optics

Problem Statement How many slits must a grating have to resolve the two sodium D-lines ($\lambda_1 = 589.0$ nm, $\lambda_2 = 589.6$ nm) in the first order? Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the…

Problem Statement Solve the oscillation/wave problem: Linearly polarized light passes through a half-wave plate with its fast axis at $22.5°$ to the polarization direction. What is the polarization state of the emerging beam? A half-wave plate rotates the polarization by $2\theta = 2\times22.5° = 45°$ relative to the fast axis. The plane of polarizatio Given…

Problem Statement In Young’s double-slit experiment ($d = 0.5$ mm, $L = 1.0$ m, $\lambda = 500$ nm), find the intensity at a point 0.75 mm from the central maximum, expressed as a fraction of $I_{max}$. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles…

Problem Statement Solve the oscillation/wave problem: Find the thickness of a half-wave plate made of quartz ($\Delta n = 0.0091$) for $\lambda = 650$ nm. $$\Delta n \cdot t = \frac{\lambda}{2} \implies t = \frac{\lambda}{2\Delta n} = \frac{650\times10^{-9}}{2\times0.0091} = \frac{650\times10^{-9}}{0.0182} \approx 35.7\;\mu\text{m} \approx \boxed{36\;\ Given Information See problem statement for all given quantities. Physical Concepts…

Problem Statement A Fabry-Perot etalon must resolve the sodium doublet ($\lambda_1 = 589.0$ nm, $\lambda_2 = 589.6$ nm). Find the minimum plate separation $d$ (reflectance $R = 0.95$, so finesse $\mathcal{F} \approx 61$). Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario…

Problem Statement Solve the optics problem: One arm of a Michelson interferometer contains an evacuated tube of length $l = 10$ cm. When the tube is filled with gas, $N = 50$ additional fringes are observed ($\lambda = 589$ nm). Find the refractive index of the gas. Extra optical path for both passes: $2(n-1)l =…

Problem Statement A soap film ($n = 1.33$, $t = 380$ nm) is illuminated at normal incidence with white light. Which wavelength in the range 400–700 nm is most strongly transmitted? Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The…

Problem Statement An air wedge has fringe spacing $\Delta x = 1.2$ mm. If one plate moves up by $\delta = 3.0\;\mu$m, how many fringes pass a fixed reference point? ($\lambda = 500$ nm) Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the…

Problem Statement Mercury yellow doublet has wavelengths $\lambda_1 = 577$ nm and $\lambda_2 = 579$ nm. In Young’s experiment, up to what order do fringes remain visible before they wash out? Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The…

Problem Statement Solve the optics problem: Newton’s rings are formed using a glass lens ($R = 1.0$ m) and a flat glass plate. With air between them, the 10th bright ring has radius $r_{10}^{air} = 2.42$ mm. The gap is filled with a liquid and the same ring has radius $r_{10}^{liq} = 2.10$ mm. Find…