Category: Part 5: Optics

Problem Statement Solve the oscillation/wave problem: A thin wire of width $b = 0.5$ mm blocks part of a plane wave ($\lambda = 500$ nm). Use Babinet’s principle to find the diffraction pattern in the forward direction. By Babinet’s principle: $U_{wire}(\theta) + U_{slit}(\theta) = U_{free}(\theta)$. In the forward direction ($\theta = 0$): $U_{free} = Given…

Problem Statement Solve the optics problem: Define the mutual coherence function $\Gamma_{12}(\tau)$ and its relation to the complex degree of coherence $\gamma_{12}(\tau)$. State the conditions for perfect coherence and incoherence. The mutual coherence function between fields at points $P_1$ and $P_2$: $$\Gamma_{12}(\tau) = \langle U^*(P_1, Given Information Refractive index $n$ or focal length $f$ as…

Problem Statement Three primary colors (R: 700 nm, G: 546 nm, B: 435 nm) are mixed in equal luminance proportions. Describe the resulting color using color-matching functions (qualitative). 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…

Problem Statement Solve the quantum/modern physics problem: A photodetector records an average of $\bar{n} = 5$ photons per pulse. Find the probability of recording exactly 0, 1, 2, and 5 photons in a single pulse. Poisson distribution: $P(n) = e^{-\bar{n}}\bar{n}^n/n!$ $$P(0) = e^{-5} = 6.74\times10^{-3} \approx \boxed{0.67\%}$$ $$P(1) = 5e^{-5} = 3.37\time Given Information Frequency…

Problem Statement A volume hologram can store one bit per $\lambda^3$ volume element. For $\lambda = 500$ nm, find the theoretical storage density in bits/cm³. 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…

Problem Statement Microwave radiation of frequency $\nu = 10$ GHz propagates through a plasma. Find the plasma frequency if the refractive index is $n = 0.95$. Plasma frequency: $\omega_p = \sqrt{n_e e^2/(\epsilon_0 m_e)}$. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts…

Problem Statement Solve the optics problem: Use the ray transfer (ABCD) matrix to find the image location for a thin lens. An object is placed at distance $u$ from a lens of focal length $f$. Find the system matrix and the image condition. System: free space ($u$) + thin lens + free space ($v$). $$M…

Problem Statement Solve the optics problem: Find the amplitude of the electric field $E_0$ in a laser beam of irradiance $I = 10^{12}$ W/m² (a femtosecond laser pulse). Compare with atomic field $E_{atom} = e/(4\pi\epsilon_0 a_0^2) \approx 5.1\times10^{11}$ V/m. $$I = \frac{n\epsilon_0 c E_0^2}{2} \implies E_0 = \sqrt{\frac{2I}{\epsilon_0 c}} Given Information Refractive index $n$ or…

Problem Statement Solve the oscillation/wave problem: Two stars are barely resolved by a telescope objective of diameter $D = 15$ cm at $\lambda = 550$ nm. Find their angular separation. At what distance would they be separated by 1 AU ($= 1.5\times10^{11}$ m)? $$\delta\theta = 1.22\frac{\lambda}{D} = 1.22\times\frac{550\times10^{-9}}{0.15} = 4.47\time Given Information Mass $m$ and…

Problem Statement A Mach-Zehnder interferometer has one arm through a gas cell of length $L = 20$ cm. When the gas pressure changes, 12 fringes shift past a reference mark ($\lambda = 589$ nm). Find the change in refractive index of the gas. Given Information All quantities, constants, and constraints stated in the problem above…