Category: Part 5: Optics

Problem Statement A straight edge is illuminated by a plane wave ($\lambda = 500$ nm). The screen is $b = 1.0$ m beyond the edge. Estimate the width of the first bright fringe in the shadow boundary region. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental…

Problem Statement A diffraction grating of width $l = 2.0$ cm has resolving power $\mathcal{R} = 45000$ in 3rd order. Find the number of slits $N$ and the slit spacing $d$. 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 telescope objective has diameter $D = 10$ cm. Find the angular resolution limit for $\lambda = 550$ nm and the minimum separation of two stars at distance $L = 1.5\times10^{11}$ km (roughly 5 pc) that can be resolved. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This…

Problem Statement Solve the work-energy problem: A microscope objective ($n = 1$, $\alpha = 30°$) is used with light $\lambda = 550$ nm. Find the minimum resolvable distance (Rayleigh criterion). Numerical aperture: NA $= n\sin\alpha = 1\times\sin30° = 0.5$. $$\delta_{min} = \frac{0.61\lambda}{NA} = \frac{0.61\times550\times10^{-9}}{0.5} = \frac{3 Given Information See problem statement for all given quantities.…

Problem Statement A circular aperture of diameter $D = 1.0$ mm is illuminated by a plane wave ($\lambda = 550$ nm). A lens of focal length $f = 100$ cm focuses the light. Find the radius of the Airy disk (first dark ring). Given Information See problem statement for all given quantities. Physical Concepts &…

Problem Statement A grating has 600 lines/mm. Find the angular dispersion $D = d\theta/d\lambda$ in the second order at $\lambda = 500$ nm. 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 the relevant conservation laws and…

Problem Statement A grating has slit width $b = 0.10$ mm and slit period $d = 0.30$ mm. Which orders of the principal maxima are missing? 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 the relevant…

Problem Statement Solve the work-energy problem: A diffraction grating with $N = 1200$ slits is used in 2nd order. Find the resolving power and the minimum resolvable wavelength difference near $\lambda = 500$ nm. $$\mathcal{R} = mN = 2 \times 1200 = \boxed{2400}$$ $$\delta\lambda_{min} = \frac{\lambda}{\mathcal{R}} = \frac{500}{2400} \approx \box Given Information See problem statement…

Problem Statement In a double-slit experiment, slit width $b = 0.08$ mm, slit separation $d = 0.25$ mm, $\lambda = 600$ nm. How many interference fringes lie within the central diffraction maximum? Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described.…

Problem Statement A diffraction grating has $N = 500$ lines/mm. Find the angles of the first three principal maxima for $\lambda = 600$ nm. 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 the relevant conservation laws…