Category: Part 5: Optics

Problem Statement Solve the work-energy problem: The Sun has radius $R_{Sun} = 6.96\times10^8$ m and surface temperature $T = 5778$ K. Find the total luminosity. Stefan-Boltzmann constant $\sigma = 5.67\times10^{-8}$ W/(m²K⁴). $$L = 4\pi R^2 \sigma T^4 = 4\pi\times(6.96\times10^8)^2\times5.67\times10^{-8}\times(5778)^4$$ $$= 4\pi\times4.84\times10 Given Information Mass $m$, velocity $v$, height $h$, or other given quantities Any forces…

Problem Statement Solve the quantum/modern physics problem: Find the energy (in eV), frequency, and wavenumber of a photon of wavelength $\lambda = 248$ nm (KrF excimer laser). $$E = \frac{hc}{\lambda} = \frac{1240\text{ eV·nm}}{248\text{ nm}} = \boxed{5.00\text{ eV}}$$ $$\nu = c/\lambda = 3\times10^8/248\times10^{-9} = \boxed{1.21\times10^{15}\text{ Hz}}$$ Given Information Frequency $\nu$ or wavelength $\lambda$ of radiation Work…

Problem Statement The Sun’s spectrum peaks at $\lambda_{max} = 502$ nm. Find the surface temperature of the Sun using Wien’s displacement law. 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 key…

Problem Statement Solve the oscillation/wave problem: Apodizing a telescope aperture with a Gaussian transmission profile $T(r) = \exp(-r^2/w^2)$ (instead of top-hat) reduces the sidelobe intensity. Qualitatively explain why, and state the trade-off. A top-hat (uniform) aperture has a hard edge, which produces strong Airy ring sidelobes (first ring $\s Given Information Mass $m$ and spring…

Problem Statement The apparent magnitude of the Sun is $m_{Sun} = -26.74$ and of the full Moon $m_{Moon} = -12.74$. Find the ratio of solar to lunar irradiance at Earth’s surface. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas…

Problem Statement Solve the quantum/modern physics problem: A femtosecond laser at $\lambda = 800$ nm is focused on a fluorescent sample to induce 2-photon excitation (2PE). If single-photon absorption occurs at $\lambda_{1p} = 400$ nm, find the energy of each photon at 800 nm and show that 2PE is energy-equivalent to 1PE. $$E_{800} = \frac{hc}{800\times10^{…

Problem Statement Solve the optics problem: Light travels through a glass rod ($n = 1.5$, length $L = 10$ cm) and then 20 cm of air. Find the total optical path length. $$OPL = n_1 L_1 + n_2 L_2 = 1.5\times10 + 1.0\times20 = 15 + 20 = \boxed{35\text{ cm}}$$ Given Information Refractive index $n$…

Problem Statement Solve the oscillation/wave problem: Sodium vapor is illuminated by sodium D light. The excited atoms reradiate. Find the natural linewidth of the D line if the upper state lifetime is $\tau = 16$ ns. Natural linewidth (Lorentzian FWHM): $$\Delta\nu_{nat} = \frac{1}{2\pi\tau} = \frac{1}{2\pi\times16\times10^{-9}} = \frac{1}{1.005\times Given Information Mass $m$ and spring constant $k$…

Problem Statement Solve the optics problem: A confocal microscope uses an objective with NA $= 1.40$ and $\lambda = 488$ nm. Find (a) the lateral resolution (Abbe limit) and (b) the axial resolution of a confocal microscope. (a) Lateral (confocal is $\sqrt{2}\times$ better than widefield): $$d_{lat} = \frac{0.61\lambda}{NA\sqrt{2}} \approx \f Given Information Refractive index $n$…

Problem Statement Solve the quantum/modern physics problem: In a 1D photonic crystal with period $\Lambda = 300$ nm ($n_1 = 1.5$, $n_2 = 1.0$, equal layer thicknesses), find the centre wavelength of the first stop band at normal incidence and estimate its bandwidth. Centre wavelength: Bragg condition $\Lambda(n_1+n_2)/2 \cdot 2 = \lambda_0$ More precisely, q…