Category: Part 5: Optics

Problem Statement White light with coherence length $l_c = 3\;\mu$m is used in a Michelson interferometer. How many fringes are visible before the coherence drops to $1/e$? ($\lambda_{avg} = 600$ nm) 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 Water droplets in a cloud have radius $r = 10\;\mu$m. For visible light $\lambda = 550$ nm, find the size parameter $x = 2\pi r/\lambda$ and determine whether Rayleigh or Mie scattering applies. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section)…

Problem Statement Solve the oscillation/wave problem: A slit of width $a = 1.0$ mm is illuminated by $\lambda = 500$ nm. Find (a) the transition distance $L_t$ between Fresnel and Fraunhofer regimes, (b) the Fresnel number at $L = 2.0$ m. (a) Transition at $N_F = 1$: $$L_t = \frac{a^2}{\lambda} = \frac{(10^{-3})^2}{500\times10^{-9}} = \frac{10^{-6}}{5\ Given…

Problem Statement A camera with aperture $f/8$ ($f = 50$ mm) focuses on an object at $u = 2.0$ m. Find the depth of field (range of object distances that produce acceptably sharp images) for a circle of confusion $c = 0.03$ mm. Given Information All quantities, constants, and constraints stated in the problem above…

Problem Statement In ellipsometry, a beam reflects off a surface at $\theta_i = 70°$. The measured ellipsometric angles are $\Psi = 15°$ and $\Delta = 130°$. Interpret these quantities and state what they determine. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical…

Problem Statement Determine the electric field for the configuration described: A Gaussian beam with $w_0 = 5$ mm and $\lambda = 1064$ nm is focused by a lens of $f = 200$ mm. Find the focused beam waist $w_0’$ and its location. Rayleigh range: $z_R = \pi w_0^2/\lambda = \pi\times(5\times10^{-3})^2/(1064\times10^{-9}) = 73.8$ m $\gg f$.…

Problem Statement Solve the oscillation/wave problem: A reconnaissance satellite at altitude $H = 400$ km uses a camera with aperture $D = 0.5$ m and $\lambda = 550$ nm. Find the ground resolution. $$\delta x = 1.22\frac{\lambda H}{D} = 1.22\times\frac{550\times10^{-9}\times4\times10^5}{0.5} = 1.22\times\frac{2.2\times10^{-1}}{0.5} = 1.22\times0.44 = \ Given Information Mass $m$ and spring constant $k$ (or…

Problem Statement A zone plate is constructed so that alternate half-period zones (not full zones) are blocked. The plate has 20 open half-zones. Find the principal focal length for $\lambda = 500$ nm if the outermost open half-zone has radius $r_{40} = 4.0$ mm and the observation point is at $b = 3.0$ m. Given…

Problem Statement A crystal plate of unknown thickness is placed between crossed polarizers. Monochromatic light at $\lambda = 589$ nm produces maximum transmission. The plate is then measured as $t = 50\;\mu$m. Find $\Delta n = |n_e – n_o|$. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as…

Problem Statement Solve the oscillation/wave problem: A grating (600 lines/mm) is illuminated at incident angle $\alpha = 45°$ in the plane containing the grating normal and the grooves, but the light also has a component out-of-plane by $\beta = 10°$. Find the position of the 1st-order diffracted beam. For conical diffraction, the grating equation gen…