BT-201 Engineering Physics - Jun 2024 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. 4 Marks
   aDefine phase velocity and group velocity.
   How to answer

   • Define phase velocity $v_p = \omega/k$.
   • Define group velocity $v_g = d\omega/dk$.
   • Give relation and physical meaning.
2. 4 Marks
   bExplain uncertainty principle.
   How to answer

   • State Heisenberg uncertainty principle.
   • Explain position-momentum form.
   • Give physical significance and example.
3. 6 Marks
   cDerive the time independent Schrödinger wave equation.
   How to answer

   • Start from time-dependent Schrodinger equation.
   • Assume separation of variables with stationary states.
   • Obtain time-independent form $-\hbar^2/2m \nabla^2\psi + V\psi = E\psi$.
4. 4 Marks
   aDefine path difference and phase difference.
   How to answer

   • Define path difference.
   • Define phase difference.
   • Give relation phase difference $= (2\pi/\lambda) \times$ path difference.
5. 4 Marks
   bWhat should be the minimum number of lines in a grating which will just resolve in the second order, the lines, whose wavelengths are $5890\mathring{A}$ and $5896\mathring{A}$.
   How to answer

   • Use grating resolving power $R = \lambda/\Delta\lambda = nN$.
   • Insert $\lambda \approx 5890 \mathring{A}$, $\Delta\lambda = 6 \mathring{A}$, $n=2$.
   • Calculate minimum $N \approx 491$.
6. 6 Marks
   cDerive the expression for intensity due to diffraction at a single slit.
   How to answer

   • Consider single slit division into secondary wavelets.
   • Integrate amplitude contributions across slit width.
   • Obtain intensity $I = I_0 (\sin\alpha/\alpha)^2$ with minima condition.
7. 4 Marks
   aExplain the Fermi level shifting in semiconductors.
   How to answer

   • Define Fermi level in intrinsic and extrinsic semiconductors.
   • Explain shift toward conduction band in n-type and valence band in p-type.
   • Show variation with temperature and doping.
8. 4 Marks
   bDiscuss the free electron theory of motors.
   How to answer

   • State assumptions of free electron theory.
   • Explain electron gas in metals.
   • Discuss conductivity and limitations.
9. 6 Marks
   cDraw the V-I characteristics of Zener diode.
   How to answer

   • Draw forward and reverse bias V-I axes.
   • Show Zener breakdown region in reverse bias.
   • Label knee voltage and breakdown voltage.
10. 4 Marks
    aExplain the properties of LASER.
    How to answer

    • Define LASER and stimulated emission basis.
    • List monochromaticity, coherence, directionality, brightness.
    • Briefly explain each property.
11. 4 Marks
    bFind the intensity of laser beam of 10 mW power and having diameter of 1.3 mW, assuming the intensity to be uniform across the beam.
    How to answer

    • Use intensity $I = Power/Area$.
    • Compute area from diameter $1.3$ mm.
    • Calculate intensity value in $W/m^2$.
12. 6 Marks
    cExplain the working of Ruby laser with labelled diagram.
    How to answer

    • Describe Ruby rod, flash lamp and resonator components.
    • Explain optical pumping and population inversion.
    • Show labelled diagram of Ruby laser with laser transition.
13. 4 Marks
    aDefine gradient of a scalar field and divergence of a vector field.
    How to answer

    • Define gradient of scalar field.
    • Define divergence of vector field.
    • Give mathematical form and physical meaning.
14. 4 Marks
    bState and prove continuity equation.
    How to answer

    • State continuity equation $\nabla \cdot \mathbf{J} + \partial\rho/\partial t = 0$.
    • Derive from conservation of charge.
    • Explain physical significance.
15. 6 Marks
    cState and explain Maxwell's equation in vacuum and non conducting medium.
    How to answer

    • Write four Maxwell equations in vacuum/non-conducting medium.
    • Explain each equation physically.
    • Give differential and integral forms.
16. 4 Marks
    aDiscuss the energy and momentum operator.
    How to answer

    • Define energy operator $i\hbar\partial/\partial t$.
    • Define momentum operator $-i\hbar\nabla$.
    • Explain use in Schrodinger equation.
17. 4 Marks
    bExplain the Dual nature of matter.
    How to answer

    • Explain wave nature via de Broglie hypothesis.
    • Explain particle nature via photoelectric effect.
    • Discuss complementarity with examples.
18. 6 Marks
    cProve that for one dimensional motion of a particle in a box $\psi_n = A\sin\frac{n\pi x}{L}$.
    How to answer

    • Solve time-independent Schrodinger equation for infinite potential box.
    • Apply boundary conditions $\psi=0$ at $0,L$.
    • Show normalized eigenfunctions $\psi_n = A\sin(n\pi x/L)$.
19. 4 Marks
    aDifferentiate between division of amplitude and division of wavefront.
    How to answer

    • Define division of amplitude.
    • Define division of wavefront.
    • Compare with examples like Michelson vs Young.
20. 4 Marks
    bIn Newton's ring experiment the diameter of $n^{th}$ and $(n+14)^{th}$ rings are 0.42 cm and 0.70 cm respectively. If the radius of curvature of plano convex lens in 100 cm. Calculate the wavelength of light.
    How to answer

    • Use Newton's ring formula $D_{n+p}^2-D_n^2 = 4p\lambda R$.
    • Insert $D_n=0.42$ cm, $D_{n+14}=0.70$ cm, $R=100$ cm.
    • Calculate $\lambda$.
21. 6 Marks
    cExplain the Michelson's interferometer experiment on the basis of labelled diagram and types of fringes.
    How to answer

    • Draw Michelson interferometer setup with source, beam splitter, mirrors.
    • Explain formation of fringes.
    • Describe circular, straight and white-light fringe types.
22. 4 Marks
    aWrite down the applications of LASER in Engineering and Medicine.
    How to answer

    • List engineering applications like cutting, welding, communication.
    • List medical applications like surgery, ophthalmology.
    • Briefly explain each use.
23. 4 Marks
    bWrite down the importance of total internal reflection in optical fiber.
    How to answer

    • Define total internal reflection condition.
    • Explain light guidance in optical fiber.
    • State importance for low-loss propagation.
24. 6 Marks
    cCalculate the numerical aperture and acceptance angle for an optical fiber, given that the refractive indices of core and cladding are 1.45 and 1.41 respectively.
    How to answer

    • Use $NA = \sqrt{n_1^2-n_2^2}$.
    • Insert $n_1=1.45$, $n_2=1.41$.
    • Compute NA and acceptance angle $\theta_a = \sin^{-1}(NA)$.