Category: Part 5: Optics

Problem Statement X-rays ($\lambda = 0.071$ nm) from a molybdenum K$\alpha$ source are reflected from crystal planes at first-order Bragg angle $\theta = 6.45°$. Find the interplanar spacing. 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…

Problem Statement Solve the oscillation/wave problem: Solve the rotational mechanics problem: A laser beam ($\lambda = 632.8$ nm) is expanded by passing through a single slit. The central maximum has half-angle $\theta_{1/2} = 0.5°$. Find the slit width. $$b = \frac{\lambda}{\sin\theta_{1/2}} = \frac{632.8\times10^{-9}}{\sin 0.5°} = \frac{632.8\times10 Given Information See problem statement for all given quantities.…

Problem Statement Solve the optics problem: Solve the optics problem: Flint glass has Verdet constant $V = 3.5$ rad/(T·m). A 10 cm rod in a field $B = 0.8$ T. Find the rotation angle. $$\phi = VBl = 3.5\times0.8\times0.10 = 0.28\text{ rad} \approx \boxed{16°}$$ Refractive index $n$ or focal length $f$ as given Object distance…

Problem Statement Solve the oscillation/wave problem: Sodium emits two lines: $\lambda_1 = 589.0$ nm and $\lambda_2 = 589.6$ nm. Find the path difference at which fringes disappear (beat length in a Michelson interferometer). All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Given Information See problem…

Problem Statement In a KDP crystal (Pockels cell), the voltage required for a $\pi/2$ phase retardation (quarter-wave voltage) is $V_{\lambda/4} = 3.4$ kV for $\lambda = 550$ nm. Find the phase retardation for $V = 1.0$ kV. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics…

Problem Statement Solve the oscillation/wave problem: Solve the oscillation/wave problem: A grating (800 lines/mm) is illuminated simultaneously by $\lambda_1 = 450$ nm and $\lambda_2 = 600$ nm. Find all orders where peaks coincide. Peaks coincide when $m_1\lambda_1 = m_2\lambda_2$, i.e., $m_1/m_2 = \lambda_2/\lambda_1 = 600/450 = 4/3$. Smallest intege Given Information $m_1/m_2 = \lambda_2/\lambda_1 =…

Problem Statement Solve the optics problem: Solve the optics problem: A Nicol prism consists of two calcite prisms cemented with Canada balsam ($n_{CB} = 1.550$). The critical angle for TIR of the ordinary ray at the calcite–balsam interface is needed. Given $n_o = 1.658$ for calcite. $$\sin\theta_c = \frac{n_{CB}}{n_o} = \frac{1.550}{1.658} Given Information See problem…

Problem Statement Quartz has $n = 1.5442$ at $\lambda = 400$ nm and $n = 1.5283$ at $\lambda = 700$ nm. Using Cauchy’s formula $n = A + B/\lambda^2$, find $A$ and $B$, then find $n$ at $\lambda = 550$ nm. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This…

Problem Statement A beam has total intensity $S_0 = 1.0$, linear polarization parameter $S_1 = 0.6$, $S_2 = 0$, $S_3 = 0$. Find the degree of polarization and the orientation of the polarization axis. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the…

Problem Statement Elliptically polarized light has the ellipse’s major-to-minor axis ratio of $E_1/E_2 = 2$, with the major axis horizontal. Find the intensities $I_{\max}$ and $I_{\min}$ through a polarizer rotated by angle $\phi$, and the degree of polarization. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental…