BT-201 Engineering Physics - Dec 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
   aExplain the wave nature of particles. Derive the time-independent Schrödinger equation for a particle in one-dimensional potential box and write its wavefunction.
   How to answer

   • de Broglie hypothesis and wave-particle duality
   • Time-independent Schrödinger equation derivation steps
   • Particle in 1D box boundary conditions and quantization
   • Wavefunction $\psi_n$ and energy expression
2. 7 Marks
   bA particle of mass $9.11\times 10^{-31}$ kg is moving in a one-dimensional box of width $10$ nm. Calculate the energy of the particle in the first three excited state.
   How to answer

   • Particle in 1D box energy formula $E_n = n^2h^2/8mL^2$
   • Identify $m$, $L$, $h$ values
   • Calculate for $n=2,3,4$ for first three excited states
   • Convert to eV and present result
3. 7 Marks
   aDescribe how Newton's ring experiment can be used to determine the refractive index of a liquid.
   How to answer

   • Newton's ring setup with liquid film
   • Condition for bright/dark rings with $\mu$
   • Diameter measurement in air vs liquid
   • Formula $\mu = (D_n^2-D_m^2)_{air}/(D_n^2-D_m^2)_{liquid}$
4. 7 Marks
   bExplain briefly the Rayleigh criterion of resolution. Discuss the resolving power of plane transmission grating and find the relation between resolving and dispersive power of the grating.
   How to answer

   • Statement of Rayleigh criterion for resolution
   • Resolving power of plane transmission grating formula
   • Dispersive power expression
   • Relation between resolving and dispersive power
5. 7 Marks
   aExplain Hall effect and derive expression for Hall voltage. Discuss its application.
   How to answer

   • Hall effect principle with magnetic deflection
   • Derivation of Hall voltage $V_H = IB/nqd$
   • Hall coefficient expression
   • Applications in carrier type and concentration
6. 7 Marks
   bExplain Fermi level for intrinsic and extrinsic semiconductors. Discuss the density of states and Bloch's theorem.
   How to answer

   • Fermi level position in intrinsic vs extrinsic semiconductors
   • Density of states concept
   • Statement of Bloch's theorem $\psi_k(r)=u_k(r)e^{ik\cdot r}$
   • Effect of doping on Fermi level
7. 7 Marks
   aDerive the relation between Einstein's coefficients (A & B) and explain the concept of population inversion.
   How to answer

   • Einstein A and B coefficients definitions
   • Rate equations at thermal equilibrium
   • Derivation using Planck's law
   • Population inversion concept and need
8. 7 Marks
   bExplain the construction and working of He-Ne laser with suitable diagram.
   How to answer

   • He-Ne laser components: discharge tube, mirrors, gas mixture
   • Energy transfer He to Ne and lasing transitions
   • Neat labelled diagram of construction
   • Working and output characteristics
9. 7 Marks
   aProve the Poynting theorem in electrodynamics and explain the physical significance of each of the term appearing in the final expression of the theorem.
   How to answer

   • Maxwell equations and Lorentz force starting point
   • Derivation of energy balance with Poynting vector $S=E\times H$
   • Identification of energy density and dissipation terms
   • Physical significance of each term
10. 7 Marks
    bDerive Maxwell's equations in vacuum.
    How to answer

    • Maxwell equations in differential/integral form
    • Vacuum conditions $\rho=0, J=0$
    • Simplified set with $\epsilon_0, \mu_0$
    • Physical meaning of each equation
11. 7 Marks
    aDiscuss the uncertainty principle. Derive the relation between group velocity and phase velocity for a free particle.
    How to answer

    • Heisenberg uncertainty principle statement
    • Group vs phase velocity definitions
    • Derivation $v_g v_p = c^2$ for free particle / $v_g = 2v_p$ non-relativistic
    • Physical interpretation
12. 7 Marks
    bCalculate the NA, Acceptance angle, Critical angle and acceptance cone, for a fiber have RI of $1.55$ and $1.50$ respectively for its core & cladding.
    How to answer

    • NA formula $NA=\sqrt{n_1^2-n_2^2}$
    • Acceptance angle $\theta_a=\sin^{-1}(NA)$
    • Critical angle $\phi_c=\sin^{-1}(n_2/n_1)$
    • Acceptance cone solid angle calculation
13. 7 Marks
    aExplain acceptance angle and acceptance cone of optical fiber. Derive expression for them.
    How to answer

    • Total internal reflection and acceptance angle definition
    • Derivation of $NA$ and $\theta_a$
    • Acceptance cone description
    • Final expressions
14. 7 Marks
    bDiscuss the phenomenon of Fraunhofer diffraction at a single slit. Show that the intensity of first subsidiary maximum is about $4.5\%$ of the principal maximum.
    How to answer

    • Single-slit Fraunhofer geometry and intensity formula
    • Condition for secondary maxima
    • Evaluation at first subsidiary maximum
    • Show ratio $\approx 0.045$ i.e. 4.5%
15. 7 Marks
    aNewton's rings are observed normally incident in reflected light of wavelength $6000$ Å. The diameter of the $10^{th}$ dark ring is $0.50$ cm, find the radius of curvature of lens and thickness of the film.
    How to answer

    • Newton's rings diameter formula $D_n^2 = 4n\lambda R$
    • Insert $\lambda=6000$ Å, $D_{10}=0.50$ cm
    • Calculate radius of curvature $R$
    • Calculate film thickness $t = D_n^2/8R$
16. 7 Marks
    bExplain Michelson interferometer and derive expression for fringe shift due to displacement of mirror.
    How to answer

    • Michelson interferometer construction and principle
    • Path difference with mirror displacement
    • Fringe shift condition $2d = n\lambda$
    • Expression $\Delta d = N\lambda/2$ for N fringes