Category: Part 5: Optics

Problem Statement Solve the oscillation/wave problem: A grating with $d = 2\;\mu$m illuminated by white light (400–700 nm). Show that the 2nd-order spectrum overlaps with the 3rd order. 2nd order range: $\sin\theta$ from $2\times400/2000 = 0.40$ to $2\times700/2000 = 0.70$. 3rd order range: $\sin\theta$ from $3\times400/2000 = 0.60$ to $3\times700/2000 Given Information See problem statement…

Problem Statement Solve the optics problem: A thin lens ($n_F = 1.515$, $n_C = 1.505$) has focal length $f_D = 20$ cm for the sodium D line. Find the chromatic aberration (separation of red and blue foci). Dispersive power: $\omega = (n_F-n_C)/(n_D-1)$. Chromatic aberration $\Delta f = f_D\,\omega$. $$\omega = \frac{n_F-n_C}{n_D-1} = \frac{0. Given Information…

Problem Statement A light source consumes $P = 60$ W of electrical power and produces a luminous flux of $\Phi = 840$ lm. Find the luminous efficacy and compare with the theoretical maximum ($683$ lm/W for 555 nm). Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental…

Problem Statement A hologram is recorded with object and reference beams from the same laser ($\lambda = 633$ nm) making an angle of $30°$ between them. Find the spatial frequency of the interference fringes recorded in the hologram. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental…

Problem Statement Solve the oscillation/wave problem: Hydrogen gas at temperature $T = 1000$ K emits the H$\alpha$ line at $\lambda = 656.3$ nm. Find the Doppler broadening $\Delta\lambda$ (FWHM). Mass of hydrogen atom $m = 1.67\times10^{-27}$ kg. Thermal velocity (Gaussian distribution, FWHM): $$v_{FWHM} = 2\sqrt{\frac{2\ln2\cdot k_B T}{m}} = 2\sqrt{\ Given Information See problem statement for…

Problem Statement A laser has coherence time $\tau_c = 10\;\mu$s. Find the spectral linewidth $\Delta\nu$ and the corresponding $\Delta\lambda$ at $\lambda = 632.8$ nm. 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 relevant conservation laws…

Problem Statement Solve the work-energy problem: The pupil of the eye has diameter $D = 3.0$ mm in bright light. Find the angular resolution limit of the eye for $\lambda = 550$ nm, and the minimum separation of two points that can be resolved at 25 cm (near point). $$\delta\theta = 1.22\frac{\lambda}{D} = 1.22\times\frac{550\times10^{-9}}{3.0\tim Given…

Problem Statement A blazed reflection grating has blaze angle $\gamma = 15°$ and is used in Littrow configuration (reflected light goes back along the incident path). Find the wavelength that is blazed most efficiently for 1st order. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics…

Problem Statement Solve the oscillation/wave problem: In Fraunhofer diffraction, the first minimum of a single slit falls at $\theta = 0.1°$ for $\lambda = 500$ nm. Find the slit width. $$b = \frac{\lambda}{\sin\theta} = \frac{500\times10^{-9}}{\sin 0.1°} = \frac{500\times10^{-9}}{1.745\times10^{-3}} \approx 2.87\times10^{-4}\text{ m} = \boxed{0.287\te Given Information See problem statement for all given quantities. Physical Concepts &…

Problem Statement A diffraction grating with $d = 2.5\;\mu$m is used with light of $\lambda = 550$ nm. What is the maximum order of diffraction that can be observed? 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…