BT-201 Engineering Physics - Jun 2022 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
   aDiscuss the physical significance of wave function.
   How to answer

   • Define wave function $\psi$ and its complex nature
   • State Born's probability interpretation of $|ψ|^2$
   • Mention conditions for a well-behaved wave function (single-valued, continuous, finite)
   • State the normalization condition $\int |\psi|^2 dV = 1$
2. 7 Marks
   bDeduce the energy Eigen values and wave function of a particle moving in one dimensional box.
   How to answer

   • Set up the 1D Schrödinger equation for $0 < x < L$
   • Apply boundary conditions $\psi(0) = 0$ and $\psi(L) = 0$
   • Derive quantized energy eigenvalues $E_n = \frac{n^2 \pi^2 \hbar^2}{2mL^2} = \frac{n^2 h^2}{8mL^2}$
   • Normalize the wave function to get $\psi_n(x) = \sqrt{\frac{2}{L}} \sin\left(\frac{n\pi x}{L}\right)$
3. 7 Marks
   aObtain the time dependent Schrodinger wave equation.
   How to answer

   • Write wave function for a free particle in terms of $p$ and $E$
   • Differentiate partially with respect to position and time
   • Identify momentum and energy operators
   • Combine using $E = \frac{p^2}{2m} + V$ to obtain $i\hbar \frac{\partial \psi}{\partial t} = -\frac{\hbar^2}{2m} \nabla^2 \psi + V\psi$
4. 7 Marks
   bDiscuss the construction and working of Michelson interferometer.
   How to answer

   • Schematic diagram showing light source, beam splitter, compensating plate, mirrors $M_1$ and $M_2$, and telescope
   • Explanation of construction details
   • Working principle based on division of amplitude
   • Condition for path difference and fringe formation
5. 7 Marks
   aWhat is superposition of waves? Explain constructive and destructive interference.
   How to answer

   • State the principle of superposition of waves ($y = y_1 + y_2$)
   • Derive expression for resultant amplitude $R = \sqrt{a_1^2 + a_2^2 + 2a_1 a_2 \cos\phi}$
   • State condition for constructive interference (phase difference $\phi = 2n\pi$, path difference $\Delta = n\lambda$)
   • State condition for destructive interference (phase difference $\phi = (2n+1)\pi$, path difference $\Delta = (2n+1)\frac{\lambda}{2}$)
6. 7 Marks
   bExplain the formation of Newton's rings. Obtain the expression to find the wavelength of light in Newton's rings experiment.
   How to answer

   • Explain experimental setup (plano-convex lens on a flat glass plate creating a wedge-shaped air film)
   • Derive relation for diameter of dark rings: $D_n^2 = 4n\lambda R$
   • Derive expression for wavelength: $\lambda = \frac{D_{n+p}^2 - D_n^2}{4pR}$
   • Draw neat diagram of experimental setup and ring formation
7. 7 Marks
   aWhat is Zener diode? Discuss its I-V characteristics.
   How to answer

   • Define Zener diode as a heavily doped p-n junction operating in reverse breakdown region
   • Sketch the complete I-V characteristic curve (forward and reverse bias)
   • Explain forward bias operation (normal diode behavior)
   • Explain reverse bias operation, breakdown voltage $V_Z$, and constant voltage property
8. 7 Marks
   bDeduce an expression for Hall coefficient and Hall voltage.
   How to answer

   • Define Hall effect with a neat diagram of semiconductor/conductor slab under electric and magnetic fields
   • Balance Lorentz force and electric force: $e E_H = e v_d B$
   • Relate current density to drift velocity: $J = n e v_d$
   • Derive Hall voltage $V_H = \frac{B I}{n e t}$ and Hall coefficient $R_H = \frac{1}{n e}$
9. 7 Marks
   aExplain the variation of Fermi level in N-type semiconductor with concentration and temperature.
   How to answer

   • Define Fermi level position in N-type semiconductor at $0\text{ K}$ (midway between $E_c$ and $E_d$)
   • Explain effect of increasing donor concentration $N_d$ (moves closer to conduction band)
   • Explain variation with temperature: low temperature (freeze-out), moderate temperature (extrinsic range), and high temperature (approaches intrinsic Fermi level $E_i$)
   • Sketch energy band diagrams showing Fermi level shift with temperature
10. 7 Marks
    bExplain the construction and working of Ruby laser with neat diagram.
    How to answer

    • Draw neat diagram of Ruby laser construction (ruby rod, flash lamp, reflective mirrors)
    • Detail construction components ($Al_2O_3$ doped with $Cr^{3+}$, cylindrical rod with silvered ends)
    • Draw three-level energy state diagram
    • Explain working: optical pumping from ground state to pump bands, non-radiative decay to metastable state, stimulated emission at $694.3\text{ nm}$
11. 7 Marks
    aDiscuss the properties of Laser light.
    How to answer

    • High degree of coherence (spatial and temporal coherence)
    • High monochromaticity (extremely narrow spectral line width)
    • High directionality (low divergence angle)
    • High intensity / brightness
12. 7 Marks
    bDeduce the expression for acceptance angle of an optical fiber. Find the acceptance angle of a fiber having core and cladding refractive indices are 1.55 and 1.50, respectively.
    How to answer

    • Derive numerical aperture and acceptance angle using Snell's law: $\theta_a = \sin^{-1}\left(\sqrt{n_1^2 - n_2^2}\right)$ for air ($n_0=1$)
    • Substitute given values: $n_1 = 1.55$, $n_2 = 1.50$
    • Calculate $\text{NA} = \sqrt{1.55^2 - 1.50^2} = \sqrt{2.4025 - 2.25} = \sqrt{0.1525} \approx 0.3905$
    • Calculate $\theta_a = \sin^{-1}(0.3905) \approx 22.98^\circ$
13. 7 Marks
    aWrite a note on different types of polarizations in dielectric materials.
    How to answer

    • Define polarization in dielectrics
    • Electronic polarization (displacement of electron cloud, temperature independent)
    • Ionic polarization (displacement of ions, temperature independent)
    • Orientational (dipolar) polarization (alignment of permanent dipoles, temperature dependent)
    • Space charge polarization (accumulation of charges at interfaces, low frequency)
    • Total polarizability $\alpha = \alpha_e + \alpha_i + \alpha_o + \alpha_s$
14. 7 Marks
    bDiscuss about the continuity equation.
    How to answer

    • State law of conservation of electric charge
    • Express total current leaving a closed surface as surface integral of $\vec{J}$
    • Equate to rate of decrease of charge within the volume $-\frac{\partial}{\partial t} \int \rho dV$
    • Apply Gauss divergence theorem to obtain $\nabla \cdot \vec{J} = -\frac{\partial \rho}{\partial t}$
    • Discuss steady-state condition where $\nabla \cdot \vec{J} = 0$
15. 14 Marks
    Write short notes on any two: a) Heisenberg's uncertainty principle b) Mach-Zehnder interferometer c) Solar cell d) V number
    How to answer

    • For Heisenberg's uncertainty principle: state $\Delta x \cdot \Delta p \ge \frac{\hbar}{2}$ and $\Delta E \cdot \Delta t \ge \frac{\hbar}{2}$ with physical meaning
    • For Mach-Zehnder interferometer: describe two beam splitters, two mirrors setup, phase shift measurement, and diagram
    • For Solar cell: describe photovoltaic effect, p-n junction under illumination, and I-V characteristics
    • For V number: define normalized frequency $V = \frac{2\pi a}{\lambda}\sqrt{n_1^2 - n_2^2}$ and its role in determining number of supported modes in an optical fiber