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MU FE Sem 1 Applied Physics Most Important Questions with Solutions (Winter 2026)

Practice set · 3 hrs 24 min · 102 marks · for MU Engineering and similar exams

2026, Winter 2026 204 minutes 102 marks Save WhatsApp

Sections

Lasers 4 Q
Fibre Optics 4 Q
Interference in Thin Films 4 Q
Electrodynamics 4 Q
Quantum Physics 4 Q
Semiconductor Physics 4 Q

What this set is

This is an original Doubtly set of 24 most important questions for the Mumbai University FE Semester 1 Applied Physics (BSC102, NEP 2020 scheme) exam in Winter 2026. It is not an official university paper and does not predict the actual paper. Questions are grouped module by module, and every question has a full step-by-step solution written by Doubtly. Marks (3 or 5) follow the way such questions are marked in recent MU papers.

How the questions were chosen

We went through the last three Applied Physics papers (December 2024, June 2025 KT and December 2025) and listed the question type behind every sub-question. Types that came in two or three of these papers were picked. Some questions are taken as-is from those papers, and their stems say which paper they came from; the rest are new questions of the same type with new numbers.

Module and question typeDec 2024June 2025 KTDec 2025
Lasers: He–Ne laser construction and workingYesYesYes
Lasers: metastable state / optical resonatorYesYesYes
Fibre optics: numerical aperture / acceptance angle derivationYesYesYes
Fibre optics: NA, critical angle, cladding index numericalsYesYesYes
Thin films: conditions for maxima and minima in reflected lightNoYesYes
Thin films: antireflection coating / film thicknessNoYesYes
Thin films: Newton's rings numericalYesYesNo
Electrodynamics: divergence of curl, curl numericalsYesYesYes
Electrodynamics: Maxwell's equation derivationsYesYesYes
Quantum: properties of matter waves / de Broglie hypothesisYesYesYes
Quantum: de Broglie wavelength, momentum and energy numericalsYesYesYes
Quantum: Schrödinger equation derivationNoYesYes
Quantum: particle in an infinite well numericalYesNoYes
Semiconductors: Fermi level lies midway in an intrinsic semiconductorYesYesYes
Semiconductors: Fermi–Dirac distribution functionYesYesNo
Semiconductors: conductivity, carrier concentration, mobility numericalsYesYesYes

The He–Ne laser, the numerical aperture (or acceptance angle) derivation and the Fermi level of an intrinsic semiconductor came in all three papers, almost word for word, and "divergence of curl is zero" came in two; these are included as-is (Q.3, Q.6, Q.22 and Q.13). Gradient of a scalar field, why an electron cannot exist in the nucleus, the uncertainty principle numerical and laser applications such as LIDAR each came once, so revise them from your notes as well.

How to use this set

Try each question on paper first, under time: about 2 minutes per mark, the pace of the real 45-mark, 90-minute exam. Then compare your working with the solution. For derivations, practise drawing the figure and writing the numbered steps; for numericals, write the formula, the substitution with units and the final answer, as the solutions do. Every numerical answer here was checked with Python.

FAQs

Are these the questions that will come in the Winter 2026 exam?

No one can promise that. These are the question types that repeated most across the last three papers, so they are the best use of revision time, but study the full syllabus too.

Why are some questions marked "asked in MU"?

Those questions were set by the university in the paper named, so you can see the exact exam wording. All other questions are new ones of the same type, and all solutions are Doubtly's own.

What is the actual exam pattern?

The recent papers are 45 marks in 1 hour 30 minutes. Q.1 has seven 3-mark questions (attempt any five, 15 marks). Q.2 to Q.5 each have three 5-mark parts, and you attempt any two of these four questions (30 marks).

Chapters covered

Instructions

Solve on paper with a timer, then check against the solutions.

Lasers

  1. Q.1 What is a metastable state? What is the role of a metastable state in a LASER? (asked in MU Dec 2024; also June 2025 KT)

    3 marks See answer →
  2. Q.2 Explain the optical resonator (resonant cavity) of a laser and its role in producing the laser beam.

    3 marks See answer →
  3. Q.3 With a neat energy level diagram, describe the construction and working of the He–Ne laser. (asked in MU June 2025 KT; also Dec 2024 and Dec 2025)

    5 marks See answer →
  4. Q.4 Explain any two industrial applications of lasers. Also explain how LIDAR works.

    5 marks See answer →

Fibre Optics

  1. Q.5 An optical fibre has a core of refractive index 1.48. It is to be clad so that total internal reflection takes place at the core–cladding interface for a ray with critical angle 80°. What is the refractive index of the cladding?

    3 marks See answer →
  2. Q.6 Derive an expression for the numerical aperture of a step index optical fibre. Give its physical significance. (asked in MU June 2025 KT; also Dec 2024)

    5 marks See answer →
  3. Q.7 The refractive indices of the core and cladding of a step index fibre are 1.50 and 1.46 respectively. Calculate (1) the numerical aperture, (2) the acceptance angle, (3) the critical angle at the core–cladding interface and (4) the fractional refractive index change.

    5 marks See answer →
  4. Q.8 Compare step index fibre and graded index fibre. (asked in MU Dec 2024)

    5 marks See answer →

Interference in Thin Films

  1. Q.9 What is an antireflection coating? State the conditions on its refractive index and thickness. Find the minimum thickness of a magnesium fluoride (\(\mu=1.38\)) antireflection coating on glass (\(\mu=1.52\)) for light of wavelength 5500 Å.

    3 marks See answer →
  2. Q.10 Find the minimum thickness of a soap film (\(\mu=1.35\)) which appears dark in reflected light of wavelength 6000 Å, when the light is incident normally on the film.

    3 marks See answer →
  3. Q.11 Obtain the conditions for maxima and minima of the light reflected from a thin transparent film of uniform thickness. (asked in MU June 2025 KT; also Dec 2025)

    5 marks See answer →
  4. Q.12 In a Newton's rings experiment the diameter of the 10th dark ring is 0.50 cm with air between the lens and the plate. When a transparent liquid is introduced between them, the diameter of the same ring becomes 0.44 cm. Find the refractive index of the liquid. Also find the radius of curvature of the lens if the wavelength of light used is 5890 Å.

    5 marks See answer →

Electrodynamics

  1. Q.13 Show that the divergence of the curl of a vector is zero. (asked in MU June 2025 KT; also Dec 2024)

    3 marks See answer →
  2. Q.14 (i) Find the curl of \(\vec A=x^2yz\,\hat i+xy^2z\,\hat j+xyz^2\,\hat k\) at the point \((1,2,-1)\). (ii) Show that \(\vec B=yz\,\hat i+zx\,\hat j+xy\,\hat k\) is irrotational.

    5 marks See answer →
  3. Q.15 State Ampere's circuital law. Derive Maxwell's fourth equation in differential form. (asked in MU June 2025 KT; also Dec 2024)

    5 marks See answer →
  4. Q.16 Deduce Maxwell's second equation in differential and integral form. (asked in MU Dec 2025)

    5 marks See answer →

Quantum Physics

  1. Q.17 State the properties of matter waves. (asked in MU Dec 2024; also Dec 2025)

    3 marks See answer →
  2. Q.18 An electron is confined in a one-dimensional potential well of width 2.5 Å with infinitely high walls. Find its energy in the ground state and in the first excited state, in joule and eV. (\(h=6.63\times10^{-34}\) J s, \(m_e=9.1\times10^{-31}\) kg)

    3 marks See answer →
  3. Q.19 Derive Schrödinger's time-independent wave equation for matter waves. (asked in MU June 2025 KT)

    5 marks See answer →
  4. Q.20 An electron and a photon each have a wavelength of 1.5 Å. Calculate their momenta and energies. (\(h=6.63\times10^{-34}\) J s, \(m_e=9.1\times10^{-31}\) kg, \(c=3\times10^8\) m/s)

    5 marks See answer →

Semiconductor Physics

  1. Q.21 Write the Fermi–Dirac distribution function and explain the terms involved in it. (asked in MU Dec 2024; also June 2025 KT)

    3 marks See answer →
  2. Q.22 Show that for an intrinsic semiconductor the Fermi level lies midway between the conduction band and the valence band. (asked in MU Dec 2024, June 2025 KT and Dec 2025)

    5 marks See answer →
  3. Q.23 The electrical conductivity of intrinsic germanium at room temperature is 2.2 mho/m. Find the intrinsic carrier concentration (electron and hole concentration). Given: mobility of electrons \(=0.39\ \text{m}^2/\text{V s}\), mobility of holes \(=0.19\ \text{m}^2/\text{V s}\).

    5 marks See answer →
  4. Q.24 Pure silicon at room temperature has an intrinsic carrier concentration of \(1.5\times10^{16}\ \text{m}^{-3}\). One out of every \(10^7\) silicon atoms is replaced by a phosphorus atom. Predict the effect on the electrical properties: find the conductivity before and after doping, and the hole concentration after doping. Given: concentration of Si atoms \(=5\times10^{28}\ \text{m}^{-3}\), \(\mu_e=0.135\ \text{m}^2/\text{V s}\), \(\mu_h=0.048\ \text{m}^2/\text{V s}\).

    5 marks See answer →