Category: Part 5: Optics

Problem Statement The solar irradiance at Earth’s surface is $E_{sun} = 1360$ W/m² (solar constant). If the Sun subtends half-angle $\alpha = 0.267°$, find the luminance (radiance) of the Sun’s disk. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The…

Problem Statement A beam is suspected to be circularly polarized. Describe how to verify this using a quarter-wave plate and a polarizer, and what result confirms circular polarization. Given Information See problem statement for all given quantities. Physical Concepts & Formulas Circular motion requires a centripetal force directed toward the centre, providing the centripetal acceleration…

Problem Statement A hologram is recorded with reference beam at angle $\alpha = 20°$ to the plate normal, using $\lambda = 633$ nm. During reconstruction with $\lambda’ = 515$ nm at the same angle, find the angle of the reconstructed image beam. Given Information See problem statement for all given quantities. Physical Concepts & Formulas…

Problem Statement Solve the oscillation/wave problem: In a double-slit experiment, the fringes are visible up to an order $m_{max} = 12$ for a source of wavelength $\lambda = 500$ nm. Estimate the coherence length of the source. All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts sectio…

Problem Statement Solve the oscillation/wave problem: A grating (600 lines/mm) is used at grazing incidence ($\theta_i = 80°$ from normal). Find the angles of the 1st-order diffracted beams for $\lambda = 600$ nm on both sides. All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section Given…

Problem Statement Four identical lamps, each of intensity $I = 60$ cd, are placed at the corners of a square of side $a = 4.0$ m. Find the illuminance at the centre of the square. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to…

Problem Statement Solve the optics problem: Solve the optics problem: Light travels through $t = 0.50$ mm of quartz ($n_e = 1.5534$, $n_o = 1.5443$) parallel to the optic axis. Find the optical path difference between e and o rays. $$\Delta = (n_e-n_o)t = (1.5534-1.5443)\times0.50\text{ mm} = 0.0091\times0.50 = 0.00455\text{ mm}$$ $$= \boxed{ Given Information…

Problem Statement Find the solid angle subtended by a circular aperture of diameter $D = 10$ cm at a distance $R = 2.0$ m from a point source. 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 Unpolarized light of intensity $I_0$ passes through three polarizers. The second is at $30°$ to the first, the third at $30°$ to the second ($60°$ total to the first). Find the final intensity. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to…

Problem Statement Solve the work-energy problem: Solve the work-energy problem: A grating with 1800 lines/mm is used in the 5th order. Find the resolving power and the minimum wavelength separation resolvable near $\lambda = 400$ nm. Length of grating needed: let’s say grating is 25 mm wide, so $N = 1800\times25 = 45000$ slits. $$\mathcal{R}…