Category: Part 5: Optics

Problem Statement Write the general intensity formula for a diffraction grating with $N$ slits, slit width $b$, and slit spacing $d$ for illumination by monochromatic light. Identify the interference and diffraction factors. 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 oscillation/wave problem: For a single slit of width $a = 0.3$ mm, $\lambda = 500$ nm, and lens focal length $f = 80$ cm, find: (a) width of central max, (b) positions of first two secondary maxima, (c) their intensities relative to central max. (a) $w_0 = 2\lambda f/a = 2\times500\times10^{-9}\times0.80/3\times10^{-4}…

Problem Statement Solve the optics problem: Verify the Newton’s lens formula $x_o x_i = f^2$ where $x_o$ and $x_i$ are object and image distances measured from the respective focal points. If object is at distance $u$ from lens, then $x_o = u – f$ (distance from front focal point). By thin lens formula: $1/v –…

Problem Statement A grating spectrometer has $N = 10000$ slits, grating spacing $d = 3\;\mu$m. Find the angular half-width of a spectral line at $\lambda = 600$ nm in 1st order. 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 Describe coma aberration in a lens and state the condition (Abbe sine condition) for its elimination. 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 is to identify which…

Problem Statement Use Fermat’s principle to derive the law of reflection for a flat mirror. Show that the path length is stationary for the reflected ray obeying $\theta_i = \theta_r$. 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 Statement Solve the optics problem: Derive Snell’s law of refraction using Fermat’s principle for a ray traveling from medium 1 ($n_1$) to medium 2 ($n_2$) across a flat interface. Optical path length: $$L(x) = n_1\sqrt{h_1^2+x^2} + n_2\sqrt{h_2^2+(D-x)^2}$$ Setting $dL/dx = 0$: $$n_1\frac{x}{\sqrt{h_1^2+x^2}} = n_2\frac{D-x}{\sqrt{h_ Given Information Refractive index $n$ or focal length $f$ as…

Problem Statement Solve the optics problem: A laser beam of power $P = 100$ mW and wavelength $\lambda = 1064$ nm is focused on a dielectric particle. Estimate the radiation pressure force on the particle if the beam is fully reflected. For full reflection, force $= 2P/c$: $$F = \frac{2P}{c} = \frac{2\times0.100}{3\times10^8} = 6.67\times10^{ Given…

Problem Statement Solve the optics problem: A glass prism (base $b = 50$ mm, $dn/d\lambda = -600$ m$^{-1}$ at $\lambda = 589$ nm) is used as a spectrometer. Find the resolving power. Resolving power of a prism spectrometer: $$\mathcal{R} = b\left|\frac{dn}{d\lambda}\right| = 0.050\times600 = \boxed{30}$$ This is quite low; $dn/d\lambda = -600 Given Information Refractive…

Problem Statement A holographic diffraction grating is 80 mm wide with 3600 lines/mm. Find the resolving power in 1st order and the minimum resolvable wavelength interval near $\lambda = 400$ nm. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas…