Category: HC Verma Part 1: Waves & Optics

Problem Statement A thin film ($n=1.5$) is surrounded by the same medium ($n=1.5$) on both sides. Phase change on reflection? 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…

Problem Statement YDSE: $d=1$ mm, $\lambda=500$ nm. Find angular positions of the first three bright fringes. 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 Newton’s Laws / mechanics problem: In Newton’s rings experiment, are the rings in transmitted light complementary to those in reflected light? Energy conservation: $I_T+I_R=I_{incident}$; patterns complementary Step 1: In transmitted light, where reflected light shows dark rings (destructive reflection), transmitted intensity is maxi Given Information Mass(es), forces, angles, and coefficients of…

Problem Statement Same as above with $\lambda=589$ nm. How many fringes shift? 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 governs…

Problem Statement YDSE: sources have amplitudes $3a$ and $a$. Find $I_{max}$ and $I_{min}$ in terms of $I_0=a^2$. 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…

Problem Statement Solve the optics problem: Air is replaced by water ($n=1.33$) in the path of one beam in an interferometer over length 2 cm. Find extra optical path. Extra OPL $=(n-1)L$ Step 1: Extra path $=(n-1)\times L=(1.33-1)\times2=0.33\times2=0.66$ cm. $$\boxed{\Delta(OPL)=0.66\text{ cm}}$$ Given Information Refractive index $n$ or focal length $f$ as given Object distance $u$…

Problem Statement Solve the oscillation/wave problem: YDSE: $d=2$ mm, $D=1.2$ m, fringe width 0.36 mm. Find $\lambda$. $\lambda=\beta d/D$ Step 1: $\lambda=\beta d/D=0.36\times10^{-3}\times2\times10^{-3}/1.2=7.2\times10^{-7}/1.2=6\times10^{-7}$ m $=600$ nm. $$\boxed{\lambda=600\text{ nm}}$$ Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial conditions (amplitude $A$, phase $\phi$) as given Physical Concepts & Formulas Simple harmonic…

Problem Statement In YDSE, bright fringe of order $n$ coincides with first diffraction minimum when slit width $a = d/n$. What is this condition? 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.…

Problem Statement Path difference between two waves is $\lambda/4$. Find the phase difference. 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 Solve the oscillation/wave problem: Newton’s rings: 10th dark ring radius = 1.59 cm, lens $R=100$ cm. Find $\lambda$. $\lambda=r_n^2/(nR)$ Step 1: $r_n^2=n\lambda R$; $\lambda=r_n^2/(nR)=(1.59\times10^{-2})^2/(10\times1)=2.53\times10^{-4}/10=2.53\times10^{-5}$ m. That is 25300 nm — too large. Check: $R=100$ cm $=1$ m; $r=1.59$ cm $=0. Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters…