Category: HC Verma Part 1: Waves & Optics

Problem Statement In YDSE, if one slit is covered, what fraction of the maximum double-slit intensity is observed at the center? 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…

Problem Statement Solve the oscillation/wave problem: A glass slab ($n=1.5$, $t=0.1$ mm) causes a shift of 83 fringes in YDSE. Find wavelength. $\lambda=(n-1)t/$fringe shift Step 1: Shift $=(n-1)t/\lambda$; $83=(0.5\times0.1\times10^{-3})/\lambda$; $\lambda=0.5\times10^{-4}/83\approx6.02\times10^{-7}$ m $\approx602$ nm. $$\boxed{\lambda\approx602\text{ Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial conditions (amplitude $A$, phase $\phi$) as given…

Problem Statement A spectral line has width $\Delta\lambda=0.01$ nm at $\lambda=500$ nm. Find the coherence length. 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 conservation law…

Problem Statement Solve the optics problem: A glass slab of thickness 1 mm in YDSE causes a shift equal to 10 fringes. $\lambda=600$ nm. Find refractive index. Fringe shift $=(n-1)t/\lambda\Rightarrow n=1+$(shift)$\lambda/t$ Step 1: Fringe shift $=(n-1)t/\lambda$; $10=(n-1)\times10^{-3}/(600\times10^{-9})$. Step 2: $(n-1)=10\times600\times10^ Given Information Refractive index $n$ or focal length $f$ as given Object distance $u$ (negative…

Problem Statement Two coherent sources have intensities $I_1=4I$ and $I_2=I$. Find fringe visibility. 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 conservation law or field equation…

Problem Statement A thin film in air ($n=1.5$) of thickness 400 nm. For which visible wavelength is there no reflection (destructive)? 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…

Problem Statement In YDSE, the source is shifted by 1 mm off axis. How does the fringe pattern change? ($S_1S_2=d=1$ mm, $D_s=1$ m from slits, screen at $D=1$ m.) 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…

Problem Statement A wedge-shaped film has an angle $\theta=0.01$ rad. Light of 600 nm is incident normally. Find the fringe spacing. 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…

Problem Statement Solve the Newton’s Laws / mechanics problem: In Newton’s rings, radii of 5th and 15th dark rings are 3.0 mm and 5.2 mm respectively. $\lambda=589$ nm. Find radius of curvature. $R=(r_m^2-r_n^2)/[(m-n)\lambda]$ from Newton’s ring measurements Step 1: $r_n^2=n\lambda R$; $r_{15}^2-r_5^2=(15-5)\lambda R$. Step 2: $R=(r_{15}^2-r_5^2)/(10\lambda)=( Given Information Mass(es), forces, angles, and coefficients of friction…

Problem Statement YDSE with equal amplitude sources, $\lambda=500$ nm. Find intensity at a point where path difference is 125 nm (express as fraction of maximum). 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…