Category: Part 5: Optics

Problem Statement Solve the optics problem: Solve the optics problem: A spectrometer measures the angle of minimum deviation of a prism ($\Theta = 60°$) for the sodium D line: $\delta_m = 37.20°$. Find $n_D$ precisely. $$n_D = \frac{\sin((\Theta+\delta_m)/2)}{\sin(\Theta/2)} = \frac{\sin(48.60°)}{\sin(30°)} = \frac{0.75011}{0.5000} = \boxed{1 Given Information See problem statement for all given quantities. Physical Concepts…

Problem Statement Solve the quantum/modern physics problem: Solve the quantum/modern physics problem: Circularly polarized light carries angular momentum of $\pm\hbar$ per photon. A beam of circular polarized light ($\lambda = 500$ nm, power $P = 1.0$ mW) is fully absorbed. Find the torque exerted on the absorber. Photon flux: $\dot{N} = P/(hc/\lambda) = P\l Given…

Problem Statement Solve the optics problem: Solve the optics problem: Green light at $\lambda_2 = 532$ nm is generated by second-harmonic generation (SHG) from a Nd:YAG laser at $\lambda_1 = 1064$ nm. Verify energy conservation and the phase-matching wavelength condition. SHG: two pump photons combine to give one SH photon. $$\hbar\omega_2 = Given Information See…

Problem Statement A TEM$_{00}$ Gaussian laser beam has beam waist $w_0 = 0.5$ mm and wavelength $\lambda = 633$ nm. Find the far-field half-angle divergence. 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…

Problem Statement Determine the electric field for the configuration described: Determine the electric field for the configuration described: Find the Rayleigh range $z_R$ for a Gaussian beam with $w_0 = 1.0$ mm at $\lambda = 1064$ nm. $$z_R = \frac{\pi w_0^2}{\lambda} = \frac{\pi\times(1.0\times10^{-3})^2}{1064\times10^{-9}} = \frac{\pi\times10^{-6}}{1.064\times10^{-6}} = \fra Given Information See problem statement for all given…

Problem Statement Solve the optics problem: Solve the optics problem: A laser cavity of length $L = 30$ cm contains a medium of refractive index $n = 1.5$. Find the longitudinal mode spacing $\Delta\nu$. Optical path length: $nL = 1.5\times0.30 = 0.45$ m. Mode spacing: $$\Delta\nu = \frac{c}{2nL} = \frac{3\times10^8}{2\times0.45} = \frac{3\ti Given Information See…

Problem Statement Solve the optics problem: Solve the optics problem: A step-index optical fiber has core $n_1 = 1.48$ and cladding $n_2 = 1.46$. Find (a) the numerical aperture, (b) the critical angle inside the fiber, (c) the acceptance angle in air. (a) $NA = \sqrt{n_1^2-n_2^2} = \sqrt{1.48^2-1.46^2} = \sqrt{2.1904-2.1316} = \sqrt{0.0588} Given Information See…

Problem Statement Solve the optics problem: Solve the optics problem: A GRIN lens has refractive index profile $n(r) = n_0(1-Ar^2/2)$ where $n_0 = 1.5$ and $A = 0.01$ mm$^{-2}$. Find the pitch length (one full period of ray oscillation). In a quadratic GRIN medium, rays follow sinusoidal paths with period: $$P = \frac{2\pi}{\sqrt{A}} = \frac{…

Problem Statement Solve the optics problem: Solve the optics problem: In a medium with refractive index $n(x,y,z) = n_0(1+\alpha y)$ where $\alpha = 0.1$ m$^{-1}$, a ray enters along the $z$-axis at $y = 0$. Describe the ray’s trajectory using the eikonal equation. The ray equation is $d/ds(n\,d\mathbf{r}/ds) = \nabla n$. Here $\nabla n =…

Problem Statement The absorption line of sodium at $\lambda = 589$ nm has optical depth $\tau = 2.5$ for a 10 cm cell of sodium vapor. Find the fraction of incident light transmitted. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario…