About this previous year paper
LASER SYSTEMS AND APPLICATIONS (NOE043)
SECTION – A
(10 × 2 = 20 Marks | Short Answers)
(a) de-Broglie wavelength of an electron
For an electron of energy V eV:
λ=h2meV=12.27V A˚\lambda = \frac{h}{\sqrt{2meV}} = \frac{12.27}{\sqrt{V}} \ \text{Å}λ=2meVh=V12.27 A˚
(b) Objective of Davisson–Germer experiment
To experimentally verify the wave nature of electrons and confirm de-Broglie’s hypothesis through electron diffraction.
(c) Unmodified radiation in Compton scattering
Unmodified radiation refers to scattered X-rays having the same wavelength as incident radiation, occurring when photons scatter without energy transfer.
(d) Stimulated emission of radiation
It is the process in which an incident photon forces an excited atom to emit another photon of the same frequency, phase, and direction, forming the basis of laser action.
(e) Role of optical cavity in a laser
The optical cavity provides multiple reflections, enhances stimulated emission, ensures directionality, and helps in achieving population inversion.
(f) Why two-level pumping is not suitable for lasing
In a two-level system, population inversion cannot be achieved because absorption and stimulated emission occur at the same rate.
(g) Spiking in ruby laser
Spiking refers to initial high-intensity pulses produced due to rapid depletion and recovery of population inversion during laser start-up.
(h) Gain medium in excimer lasers
The gain medium is an excited dimer (excimer) such as ArF, KrF, or XeCl formed temporarily during laser action.
(i) Role of Q-switching
Q-switching allows storage of energy in the gain medium and its sudden release, producing very high-power, short laser pulses.
(j) Characteristics of a hologram
A hologram:
Stores amplitude and phase information
Produces a 3D image
Each part contains information of the whole object
SECTION – B
(Attempt Any Five | 5 × 10 = 50 Marks)
(a) Heisenberg Uncertainty Principle & Binding Energy
The uncertainty principle states:
ΔxΔp≥h4π\Delta x \Delta p \ge \frac{h}{4\pi}ΔxΔp≥4πh
Significance:
For microscopic particles, uncertainty is significant
For macroscopic bodies, it is negligible
Binding Energy of Electron:
Using uncertainty principle, minimum energy of electron in atom is obtained, showing stable bound states exist.
(b) Components and Principle of Laser + Coherence Length
Main Components:
Active medium
Pumping source
Optical resonator
Principle:
Population inversion + stimulated emission → coherent laser beam.
Coherence Length:
L=cΔν=3×1083000=1×105 mL = \frac{c}{\Delta \nu} = \frac{3\times10^8}{3000} = 1\times10^5 \text{ m}L=Δνc=30003×108=1×105 m
(c) Advantages of Four-Level Lasers & Threshold Power
Advantages:
Easier population inversion
Lower threshold pumping power
Continuous operation possible
Threshold Pumping Power (3-level):
Derived using rate equations; it is higher than four-level systems due to ground-state pumping.
(d) Classification of Lasers Based on Medium
Solid-state lasers (Ruby, Nd:YAG)
Gas lasers (He-Ne, CO₂)
Liquid lasers (Dye lasers)
Semiconductor lasers
Each has specific advantages and limitations regarding efficiency, wavelength range, and power.
(e) CO₂ Laser – Construction & Photon Calculation
Construction: Gas mixture of CO₂, N₂, He
Working: Energy transfer from N₂ → CO₂ → laser emission
Number of photons:
E=hcλE = \frac{hc}{\lambda}E=λhc N=PEN = \frac{P}{E}N=EP
(Substituting given values gives total photons per second.)
(f) Mode Locking
Mode locking forces all longitudinal modes to oscillate in phase, producing ultra-short pulses (picoseconds).
(g) Dye Lasers
Dye lasers use organic dyes in liquid form as gain medium.
Features:
Wide tunability
High efficiency
Short pulse generation
(h) LIDAR – Principle & Applications
Principle:
Laser pulses are emitted and reflected from targets; distance is calculated using time of flight.
Applications:
Atmospheric monitoring
Range finding
Pollution measurement
Remote sensing
SECTION – C
(Attempt Any Two | 2 × 15 = 30 Marks)
3) Particle in a One-Dimensional Box
Schrödinger Equation:
−h28π2md2ψdx2=Eψ-\frac{h^2}{8\pi^2m}\frac{d^2\psi}{dx^2}=E\psi−8π2mh2dx2d2ψ=Eψ
Eigenvalues:
En=n2h28mL2E_n=\frac{n^2h^2}{8mL^2}En=8mL2n2h2
For L = 1 Å:
E1=37.6 eV,E2=150.4 eVE_1 = 37.6\ \text{eV}, \quad E_2 = 150.4\ \text{eV}E1=37.6 eV,E2=150.4 eV
This proves energy levels are discrete.
4) Solid-State Lasers & Alexandrite Laser
Alexandrite Laser:
Tunable solid-state laser
Chromium-doped BeAl₂O₄ crystal
Advantages over Nd:YAG:
Wider tunability
Higher peak power
Better thermal properties
Applications: medical, spectroscopy, research.
5)
(i) Lasers in Drilling, Cutting & Melting
Lasers provide high precision, minimal heat-affected zone, and non-contact machining.
(ii) Laser Characteristics for Length Measurement
High coherence
Monochromaticity
Directionality
Method: Interferometry using stable laser source.