BT-201 Engineering Physics - Jun 2025 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aDerive time dependent and time independent Schrodinger wave equation.
   How to answer

   • Wave function expression for a free particle in 1D/3D
   • Differentiating with respect to space to relate momentum $p$
   • Differentiating with respect to time to relate energy $E$
   • Combining via $E = \frac{p^2}{2m} + V$ to obtain time-dependent equation
   • Separation of variables to obtain time-independent equation
2. 7 Marks
   bDiscuss the physical significance of wave function.
   How to answer

   • Meaning of wave function $\psi$ and probability amplitude
   • Born's interpretation: $|\psi|^2$ represents probability density
   • Conditions for a well-behaved wave function (single-valued, continuous, finite)
   • Normalization condition $\int |\psi|^2 dV = 1$
3. 7 Marks
   aDescribe the construction and working of Mach-Zehnder interferometer.
   How to answer

   • Schematic diagram of Mach-Zehnder setup showing two beam splitters and two mirrors
   • Description of components (BS1, BS2, M1, M2, detectors/screen)
   • Working principle and path separation into two arms
   • Applications (refractive index changes, phase shift measurements)
4. 7 Marks
   bWhat is superposition of wave and interference of light by amplitude splitting?
   How to answer

   • Principle of superposition of waves ($y = y_1 + y_2$)
   • Definition of interference of light
   • Concept of division/splitting of amplitude (partial reflection and transmission)
   • Examples of amplitude splitting (thin films, Michelson interferometer)
5. 7 Marks
   aExplain the Numerical aperture and acceptance angle of Optical Fiber.
   How to answer

   • Definition of acceptance angle $\theta_0$
   • Definition of numerical aperture (NA)
   • Ray diagram showing light entering fiber and undergoing total internal reflection
   • Formulas: $\theta_0 = \sin^{-1}(\sqrt{n_1^2 - n_2^2}/n_0)$ and $\text{NA} = \sqrt{n_1^2 - n_2^2}$
6. 7 Marks
   bExplain the construction and working of Ruby laser with neat diagram.
   How to answer

   • Neat schematic diagram of ruby laser setup (ruby rod, xenon flash lamp, resonator mirrors)
   • Components: active medium ($Al_2O_3 : Cr^{3+}$), optical cavity, pumping source
   • Three-level energy state diagram explaining absorption, non-radiative transition, and laser transition (694.3 nm)
   • Working steps explaining population inversion and stimulated emission
7. 7 Marks
   aExplain Maxwell's equations in vacuum.
   How to answer

   • State conditions for vacuum: $\rho = 0$ and $\vec{J} = 0$
   • Write differential forms: $\nabla \cdot \vec{E} = 0$, $\nabla \cdot \vec{B} = 0$, $\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$, $\nabla \times \vec{B} = \mu_0 \varepsilon_0 \frac{\partial \vec{E}}{\partial t}$
   • Physical explanation of each equation in vacuum
8. 7 Marks
   bWrite a note on different types of polarization in dielectric materials.
   How to answer

   • Definition of dielectric polarization $\vec{P}$
   • Electronic polarization (displacement of electron cloud) with formula $\alpha_e$
   • Ionic polarization (displacement of cations and anions) with formula $\alpha_i$
   • Orientational (dipolar) polarization with temperature dependence $\alpha_o \propto 1/T$
   • Space charge polarization and total polarizability $\alpha = \alpha_e + \alpha_i + \alpha_o + \alpha_s$
9. 7 Marks
   aStarting from the principle of charge conservation, derive the continuity equation for current densities in a conducting medium. Clearly state all assumptions and intermediate steps in your derivation.
   How to answer

   • State law of conservation of charge: rate of decrease of charge within a volume equals outbound current
   • Write $I = \oint_S \vec{J} \cdot d\vec{A} = -\frac{d}{dt} \int_V \rho dV$
   • Apply Gauss's Divergence Theorem: $\oint_S \vec{J} \cdot d\vec{A} = \int_V (\nabla \cdot \vec{J}) dV$
   • Combine into $\int_V \left(\nabla \cdot \vec{J} + \frac{\partial \rho}{\partial t}\right) dV = 0$
   • Conclude $\nabla \cdot \vec{J} + \frac{\partial \rho}{\partial t} = 0$ for an arbitrary volume
10. 7 Marks
    bWhat are the Einstein coefficients? Derive the relationship between Einstein coefficients A and B.
    How to answer

    • Define $B_{12}$ (absorption), $A_{21}$ (spontaneous emission), and $B_{21}$ (stimulated emission)
    • Formulate rate equations at thermal equilibrium: $N_1 B_{12} u(\nu) = N_2 A_{21} + N_2 B_{21} u(\nu)$
    • Use Boltzmann distribution $N_2/N_1 = e^{-h\nu/kT}$
    • Compare resulting radiation density $u(\nu)$ with Planck's radiation formula
    • Obtain relations: $B_{12} = B_{21}$ and $A_{21}/B_{21} = 8\pi h\nu^3 / c^3$
11. 7 Marks
    aWhat is the importance of Rayleigh criteria. Explain Rayleigh criterion for limit of resolution.
    How to answer

    • Importance of Rayleigh criterion in determining resolving power of optical instruments
    • Statement of Rayleigh's criterion: central maximum of one coincides with first minimum of other
    • Intensity distribution diagrams for well-resolved, just resolved, and unresolved conditions
    • Mathematical expressions for circular aperture/grating
12. 7 Marks
    bExplain Construction and working of $\text{CO}_2$ LASER with suitable energy level diagram.
    How to answer

    • Construction: discharge tube containing mixture of $\text{CO}_2$, $\text{N}_2$, and $\text{He}$ gases, optical resonator
    • Vibrational modes of $\text{CO}_2$ molecule (symmetric stretching, bending, asymmetric stretching)
    • Energy level diagram showing resonant energy transfer from $\text{N}_2$ to $\text{CO}_2$
    • Working and laser emission at $10.6\;\mu\text{m}$ and $9.6\;\mu\text{m}$
13. 7 Marks
    aWhat is Zener diode? Discuss its V-I Characteristics.
    How to answer

    • Definition of Zener diode (heavily doped p-n junction operating in reverse breakdown)
    • Draw V-I characteristic curve (forward bias and reverse bias showing Zener breakdown voltage $V_Z$)
    • Explanation of forward bias behavior and reverse breakdown region
    • Applications (voltage regulator)
14. 7 Marks
    bExplain in detail the working of Michelson's interferometer.
    How to answer

    • Schematic diagram of Michelson interferometer (source, beam splitter, compensating plate, mirrors M1 and M2, telescope)
    • Principle of division of amplitude into two coherent beams
    • Optical path difference formula: $\Delta = 2d \cos r$
    • Formation of circular and localized straight fringes
    • Applications (wavelength determination, thickness measurement)
15. 14 Marks
    Write short notes on the following:

    1. a)Solar cell
    2. b)Hall effect
    3. c)Bloch's theorem
    How to answer

    • Solar cell: Photovoltaic effect, p-n junction structure, generation, separation, collection, V-I curve
    • Hall effect: Concept of transverse voltage in presence of magnetic field, Hall voltage $V_H$, Hall coefficient $R_H = 1/(ne)$, applications
    • Bloch's theorem: Electron motion in a periodic potential of a crystal lattice, wave function form $\psi_k(\vec{r}) = e^{i\vec{k}\cdot\vec{r}} u_k(\vec{r})$ where $u_k$ has lattice periodicity