Category: Part 5: Optics

Problem Statement In a 3-level laser system (e.g., ruby), explain why the threshold pump power is higher than in a 4-level system, and calculate the minimum fraction of atoms that must be pumped to the upper level for inversion. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as…

Problem Statement Solve the quantum/modern physics problem: An X-ray photon ($\lambda = 0.0710$ nm) Compton scatters off a free electron at angle $\theta = 90°$. Find the wavelength shift and the kinetic energy of the recoiling electron. $$\Delta\lambda = \frac{h}{m_e c}(1-\cos\theta) = 2.426\text{ pm}\times(1-0) = 2.426\text{ pm}$$ $$\lambda’ = 71.0+2.43 = Given Information Frequency $\nu$…

Problem Statement Solve the quantum/modern physics problem: A laser beam of power $P = 1.0$ W is absorbed by a perfectly black surface. Find the radiation pressure force and the pressure in Pa if the beam area is $A = 1.0$ cm². Force (for full absorption): $F = P/c = 1.0/(3\times10^8) = 3.33\times10^{-9}$ N $=…

Problem Statement Solve the quantum/modern physics problem: The photoelectric threshold wavelength for sodium is $\lambda_0 = 540$ nm. Find the work function and the maximum kinetic energy of electrons ejected by light at $\lambda = 400$ nm. $$W = hc/\lambda_0 = 1240/540\text{ nm·eV} = 2.30\text{ eV}$$ $$KE_{max} = hc/\lambda – W = 1240/400 – 2.30…

Problem Statement Solve the quantum/modern physics problem: A silicon photodetector ($E_g = 1.12$ eV) is illuminated by light of wavelength $\lambda = 900$ nm. (a) Does the photon have enough energy to create an electron-hole pair? (b) What is the maximum wavelength for detection? (a) Photon energy: $E = hc/\lambda = (6.626\times10^{-34}\times3\times10^8)/(9 Given Information Frequency…

Problem Statement The Fried parameter $r_0 = 10$ cm for visible light at an observatory site. This sets the diffraction-limited resolution of a ground-based telescope. For a 4 m telescope at $\lambda = 550$ nm, compare the seeing-limited and diffraction-limited angular resolutions. Given Information All quantities, constants, and constraints stated in the problem above Physical…

Problem Statement Solve the optics problem: A 4-level laser medium has stimulated emission cross section $\sigma = 3\times10^{-23}$ m² and upper state lifetime $\tau = 1\;\mu$s. The cavity has length $L = 0.3$ m, output coupler $R = 0.95$, and internal loss $\alpha_i = 0.1$ m$^{-1}$. Find the threshold population inversion density. Threshold Given Information…

Problem Statement Solve the oscillation/wave problem: A sinusoidal phase grating has transmission function $t(x) = e^{i\Delta\phi\sin(2\pi x/d)}$ where $\Delta\phi = 1.5$ rad and $d = 10\;\mu$m. Find the relative intensities of the 0th, ±1st, and ±2nd orders for $\lambda = 500$ nm. Expanding using Jacobi-Anger: the amplitude in order $m$ is $J_m(\Delta Given Information Mass…

Problem Statement Solve the quantum/modern physics problem: A photodetector receives $N = 10^6$ photons per second at $\lambda = 500$ nm. Find (a) the photocurrent for quantum efficiency $\eta = 0.8$, (b) the shot noise current (RMS) in a bandwidth $\Delta f = 1$ Hz. (a) Photocurrent: $I = \eta N e = 0.8\times10^6\times1.6\times10^{-19} =…

Problem Statement In an HBT experiment, two detectors are placed symmetrically. For thermal light, the intensity correlation $g^{(2)}(0) = 2$, while for coherent (laser) light $g^{(2)}(0) = 1$. Explain the physical meaning. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts &…