BPHCT 137 Waves and Optics key facts
- Course code: BPHCT 137 (printed BPHCT-137)
- Subject: Waves and Optics
- Programme: Bachelor of Science (General) BSCG and Bachelor of Science (Multidisciplinary) BSCM
- Course type: Physics Discipline Specific Core theory course
- Credits: 4 (theory); companion lab BPHCL 138 Waves and Optics Laboratory is a separate 2 credit course
- Blocks / units: 4 blocks and 14 units (Block 1: Units 1 to 5; Block 2: Units 6 to 8; Block 3: Units 9 to 11; Block 4: Units 12 to 14)
- Maximum marks: 50
- Duration: 2 hours
- Questions in the June 2026 paper: 5 questions with 15 parts; attempt any 2 parts of each question (10 parts)
- Samples shown on this page: 2 (Q1(a) and Q2(c))
- Questions in the paid file: All 15 parts solved, including the 13 not shown on this page
What the BPHCT 137 Solved Question Paper June 2026 covers
BPHCT 137 Solved Question Paper June 2026 gives worked answers to all 15 parts of the June 2026 term-end paper, with two of them shown on this page.
BPHCT 137 Waves and Optics is a Physics Discipline Specific Core course in IGNOU's Bachelor of Science (General) BSCG and Bachelor of Science (Multidisciplinary) BSCM programmes. It runs from sound waves and beats through interference, diffraction and polarisation to lasers and optical fibres.
We took the official June 2026 BPHCT 137 Question Paper and our physics experts solved every part in the length and layout IGNOU examiners expect. Numericals carry units at each step, derivations are not skipped, and the diagrams the paper names are drawn and labelled.
The answers follow the four blocks of the official self learning material, which you can browse on eGyanKosh (BPHCT-137, Hindi medium blocks). Because we studied earlier papers first, the file also shows you which Waves and Optics topics keep coming back.
BPHCT 137 sample solved questions: two Waves and Optics answers in full
Two complete answers from the June 2026 paper are below: one numerical on beats and one derivation on superposition.
These two show exactly how the rest of the file is written. Read them, then decide whether you want the remaining 13 parts.
Question 1(a) (5 marks)
65 tuning forks are arranged in increasing order of their frequency and any two successive forks produce 4 beats per second when sounded together. Calculate the frequency of first tuning fork if the frequency of the last tuning fork is twice of it.
Answer
Given: number of forks N = 65; beats between any two successive forks = 4 per second; frequency of the last fork = 2 Γ frequency of the first fork.
Idea: Beats per second equal the difference of the two frequencies. Since the forks are in increasing order and each pair differs by 4 Hz, the frequencies form an arithmetic progression with common difference d = 4 Hz.
Step 1. Let the frequency of the first fork be n. The frequency of the k-th fork is n + (k β 1)d, so the 65th fork has frequency n + (65 β 1) Γ 4 = n + 256.
Step 2. The question states that the last fork has twice the frequency of the first: n + 256 = 2n.
Step 3. Solving, n = 256 Hz. The last fork therefore has frequency 2 Γ 256 = 512 Hz.
Check: 512 β 256 = 256 Hz, and 64 gaps Γ 4 Hz = 256 Hz. The values agree.
Answer: Frequency of the first tuning fork = 256 Hz (and the last fork = 512 Hz).
Examiner tip: Count the gaps, not the forks. Sixty five forks have only 64 gaps between them, and using 65 is the most common mistake in this BPHCT 137 numerical.
Question 2(c) (5 marks)
It two waves having equal frequencies and constant phase difference are travelling in the same direction, show that when they superpose, the intensity of the resultant wave in given by : I = a12 + a22 + 2a1a2 cos Ο where a1 and a2 are amplitudes of the constituent waves and Ο is the phase difference.
Answer
Setting up the waves. Take two waves of the same angular frequency Ο travelling in the same direction, with amplitudes a1 and a2 and a constant phase difference Ο. At a given point their displacements are y1 = a1 sin Οt and y2 = a2 sin (Οt + Ο).
Superposition. By the principle of superposition, the resultant displacement is y = y1 + y2. Expanding sin (Οt + Ο) gives y = a1 sin Οt + a2 sin Οt cos Ο + a2 cos Οt sin Ο.
Grouping terms: y = (a1 + a2 cos Ο) sin Οt + (a2 sin Ο) cos Οt. β¦(1)
Introducing the resultant. Put a1 + a2 cos Ο = A cos ΞΈ β¦(2) and a2 sin Ο = A sin ΞΈ β¦(3). Equation (1) becomes y = A (sin Οt cos ΞΈ + cos Οt sin ΞΈ) = A sin (Οt + ΞΈ).
So the resultant is also a simple harmonic wave of the same frequency Ο, with amplitude A and phase ΞΈ, where tan ΞΈ = a2 sin Ο / (a1 + a2 cos Ο).
Finding the amplitude. Squaring and adding (2) and (3): A2 = (a1 + a2 cos Ο)2 + a22 sin2 Ο = a12 + 2a1a2 cos Ο + a22(cos2 Ο + sin2 Ο).
Since cos2 Ο + sin2 Ο = 1, A2 = a12 + a22 + 2a1a2 cos Ο.
Intensity. Intensity is proportional to the square of the amplitude. Taking the constant of proportionality as unity, I = A2, so I = a12 + a22 + 2a1a2 cos Ο, which is the required result.
Interpreting the result. When Ο = 0, 2Ο, 4Οβ¦, cos Ο = 1 and Imax = (a1 + a2)2, giving constructive interference. When Ο = Ο, 3Ο, 5Οβ¦, cos Ο = β1 and Imin = (a1 β a2)2, giving destructive interference.
For equal amplitudes a1 = a2 = a, I = 2a2(1 + cos Ο) = 4a2 cos2(Ο/2), so intensity swings between 4a2 and zero.
The term 2a1a2 cos Ο is the interference term. If Ο changed randomly with time it would average to zero and the intensities would simply add, which is why a constant phase difference, that is coherent sources, is essential for steady fringes. Energy is not lost, only redistributed between bright and dark regions.
Questions answered only in the full file
The 13 parts below are printed exactly as they appear in the June 2026 paper. Their worked answers are available only in the full solved file.
- Q1(b) On a Sitar string of length 1.0 m, fundamental mode and next two harmonics of a standing wave are generated. Calculate the frequencies of these modes. Take speed of waves on the string as 2.5 Γ 103 msβ1.
- Q1(c) What is a Nicol prism ? Discuss how linearly polarized light is obtained using a Nicol Prism.
- Q2(a) Discuss the conditions under which fringes of equal inclination and equal thickness are obtained.
- Q2(b) With the help of a line diagram, discuss the working of Michelson interferometer.
- Q3(a) Discuss the uses of lasers in basic research and environmental monitoring.
- Q3(b) The velocity of light in the core of a step index fibre is 2 Γ 108 msβ1 and critical angle is 80ΒΊ. Calculate the Numerical Aperture (NA) and acceptance angle for the fibre in air. Consider velocity of light in air to be 3 Γ 108 msβ1.
- Q3(c) What do you understand by population inversion ? Discuss its role in operation of lasers.
- Q4(a) Consider a diffraction grating with 15000 lines per inch. Calculate the angular separation of D1 and D2 lines of sodium in the 2nd order. Given : Ξ»D1 β Ξ»D2 = 6Γ .
- Q4(b) Starting from the expression for the amplitude E1 of electric field produced by one of the slits at a point PΞΈ, E1 = A (sin Ξ² / Ξ²) cos (Οt β Ξ²), where Ξ² = Οb sin ΞΈ / Ξ», obtain the expression for intensity of double slit diffraction pattern. Identify the interference and diffraction terms.
- Q4(c) In the experimental setup for obtaining Fraunhofer diffraction pattern of a vertical slit, consider that the slit width b has values b = 10Ξ», 4Ξ» and Ξ». Calculate the spread of the central maximum for each value of slit width.
- Q5(a) A thin glass sheet of refractive index (ΞΌ) 1.6 is introduced normally in the path of one of the two interfering waves. The central bright fringe is observed to shift to the position originally occupied by the eight bright fringes. The source of light is monochromatic and emits light of wavelength 6000Γ . Determine the thickness of the glass sheet.
- Q5(b) Depict refractive index profiles of step index multimode and graded index multimode optical fibres. Also plot propagating modes for these fibers.
- Q5(c) The first order principal maximum of light of wavelength 656 nm is at ΞΈ = 18ΒΊ for a particular grating. (i) Calculate the slit spacing of the grating. (ii) Using the same grating, the first-order principal maximum of another source of light is observed at ΞΈ = 15.7ΒΊ. What is the wavelength of light ?
BPHCT 137 Waves and Optics block wise syllabus
BPHCT 137 is taught in four blocks: Waves, Interference, Diffraction, and Lasers and Optical Fibres.
The course has 14 units spread over four blocks. Topics in each row are the ones IGNOU actually examines from that block, taken from the official papers. Pair this with our BPHCT 137 Study Material for block by block revision.
| Block | Block title | Units | Topics examined from this block | June 2026 parts |
|---|---|---|---|---|
| Block 1 | Waves: An Introduction | Units 1 to 5 | Beats between tuning forks; standing waves and harmonics on a sitar or guitar string; Nicol prism, Malus' law and birefringence in Unit 5, Polarisation of Light | Q1(a), Q1(b), Q1(c) |
| Block 2 | Interference | Units 6 to 8 | Superposition and resultant intensity; fringes of equal inclination and equal thickness; Michelson interferometer; fringe shift by a thin glass sheet | Q2(a), Q2(b), Q2(c), Q5(a) |
| Block 3 | Diffraction | Units 9 to 11 | Single slit Fraunhofer central maximum; double slit intensity with interference and diffraction terms; grating resolution of sodium D1 and D2 lines | Q4(a), Q4(b), Q4(c), Q5(c) |
| Block 4 | Lasers and Optical Fibres | Units 12 to 14 | Population inversion and pumping; laser uses in research and pollution monitoring; numerical aperture, acceptance angle and step versus graded index profiles | Q3(a), Q3(b), Q3(c), Q5(b) |
How the BPHCT 137 question paper is set: pattern and marks
The June 2026 BPHCT 137 paper has five compulsory questions, each offering three 5 mark parts, of which you answer any two.
That makes 10 answers in 2 hours for 50 marks, roughly 12 minutes per part. Calculators are allowed and the booklet carries the same paper in Hindi.
| Question | Main area | Choice | Marks |
|---|---|---|---|
| Q1 | Beats, string harmonics, Nicol prism | Any 2 of 3 | 2 Γ 5 = 10 |
| Q2 | Fringes, Michelson interferometer, superposition intensity | Any 2 of 3 | 2 Γ 5 = 10 |
| Q3 | Laser uses, fibre numerical aperture, population inversion | Any 2 of 3 | 2 Γ 5 = 10 |
| Q4 | Grating D lines, double slit intensity, single slit spread | Any 2 of 3 | 2 Γ 5 = 10 |
| Q5 | Glass sheet fringe shift, fibre profiles, grating spacing | Any 2 of 3 | 2 Γ 5 = 10 |
Watch the change in format. December 2021, December 2022, June 2025 and December 2025 all opened with eight short 2 mark parts (attempt five), and December 2024 had one 10 mark either-or question. June 2026 drops both and uses 5 mark parts throughout. Compare the layouts yourself on our IGNOU Previous Year Question Paper page.
Numericals made up 7 of the 15 June 2026 parts. Students who can handle beats, harmonics, numerical aperture and grating equations confidently can secure close to half the paper on calculation alone.
Most repeated BPHCT 137 important questions topics
Across six official BPHCT 137 papers, six topic areas appeared in every single session.
We counted each topic once per session, however many parts it took, using the December 2021, December 2022, December 2024, June 2025, December 2025 and June 2026 papers from IGNOU's own servers.
| Topic | Block | Sessions where it appeared | Count (of 6) |
|---|---|---|---|
| Michelson interferometer (working, circular fringes, sodium doublet) | 2 | Dec 2021, Dec 2022, Dec 2024, June 2025, Dec 2025, June 2026 | 6 |
| Standing waves and harmonics on a stretched string | 1 | Dec 2021, Dec 2022, Dec 2024, June 2025, Dec 2025, June 2026 | 6 |
| Polarisation: Nicol prism, calcite birefringence, Malus' law | 1 (Unit 5) | Dec 2021, Dec 2022, Dec 2024, June 2025, Dec 2025, June 2026 | 6 |
| Thin film, air wedge, Newton's rings, equal inclination and thickness fringes | 2 | Dec 2021, Dec 2022, Dec 2024, June 2025, Dec 2025, June 2026 | 6 |
| Optical fibre index profiles, modes, dispersion, numerical aperture | 4 | Dec 2021, Dec 2022, Dec 2024, June 2025, Dec 2025, June 2026 | 6 |
| Laser components, pumping schemes, population inversion, laser types | 4 | Dec 2021, Dec 2022, Dec 2024, June 2025, Dec 2025, June 2026 | 6 |
| Fresnel half period zones and the zone plate | 3 | Dec 2021, Dec 2022, Dec 2024, June 2025, Dec 2025 | 5 |
| Grating principal maxima and lines per inch numericals | 3 | Dec 2021, Dec 2022, June 2025, Dec 2025, June 2026 | 5 |
| Superposition intensity and maximum to minimum intensity ratio | 2 | Dec 2021, Dec 2022, Dec 2024, June 2025, June 2026 | 5 |
| Double slit diffraction pattern | 3 | Dec 2022, June 2025, Dec 2025, June 2026 | 4 |
| Single slit Fraunhofer diffraction | 3 | Dec 2021, Dec 2024, June 2025, June 2026 | 4 |
| Coherence length and coherence time | 4 | Dec 2021, Dec 2024, Dec 2025 | 3 |
| Laser applications in research and communication | 4 | Dec 2021, June 2025, June 2026 | 3 |
Three June 2026 parts were asked almost word for word before: the Nicol prism (Dec 2021, June 2025), Michelson interferometer working (Dec 2021, June 2025) and the superposition intensity proof (Dec 2021, June 2025). For a wider shortlist across courses, see our IGNOU Important Questions collection.
One surprise: the zone plate, asked in five straight sessions we checked, did not appear in June 2026. Topics that skip a session often return in the next, so do not drop it for December 2026.
How our Waves and Optics answers are worked and checked
Each answer is solved by a physics expert, recalculated by a second person, then reviewed against the paper before release.
Every part of the IGNOU BPHCT 137 Solved Question Paper goes through the same two person process, so the 13 locked answers match the quality of the two samples above.
Numericals follow a fixed order: given data in SI units, the governing relation, substitution, result with units, and a one line check. In Q3(b), for example, the core index comes from the speed of light before numerical aperture is touched, and the file shows why that order matters.
Derivations such as Q4(b) are written so each line follows from the last, ending with the interference factor cos2 Ξ³ and the diffraction factor (sin Ξ² / Ξ²)2 named clearly, since IGNOU awards marks for identifying them.
Diagrams are drawn simply enough to reproduce in an exam hall: the Michelson set-up with its compensating plate, and step versus graded index profiles with ray paths. Students preparing other physics papers can use the same approach with any BSCG Question Paper in our collection.
BPHCT 137 solved file index: all 15 parts by block
The full file solves all 15 parts; 2 are on this page and 13 are in the full file only.
BPHCT 137 is a theory course, so this index replaces a practical file list. It maps every printed part to its course block and shows where its answer sits.
| Part | What it asks | Block | Answer |
|---|---|---|---|
| Q1(a) | First tuning fork frequency from 4 beats per second | Block 1 | On this page |
| Q1(b) | Fundamental and next two harmonics on a 1.0 m sitar string | Block 1 | Full file only |
| Q1(c) | Nicol prism and linearly polarised light | Block 1 | Full file only |
| Q2(a) | Conditions for equal inclination and equal thickness fringes | Block 2 | Full file only |
| Q2(b) | Michelson interferometer with line diagram | Block 2 | Full file only |
| Q2(c) | Resultant intensity of two superposed waves | Block 2 | On this page |
| Q3(a) | Laser uses in research and environmental monitoring | Block 4 | Full file only |
| Q3(b) | Numerical aperture and acceptance angle, critical angle 80ΒΊ | Block 4 | Full file only |
| Q3(c) | Population inversion and its role in lasers | Block 4 | Full file only |
| Q4(a) | Angular separation of sodium D lines, 15000 lines per inch | Block 3 | Full file only |
| Q4(b) | Double slit diffraction intensity expression | Block 3 | Full file only |
| Q4(c) | Central maximum spread for b = 10Ξ», 4Ξ» and Ξ» | Block 3 | Full file only |
| Q5(a) | Glass sheet thickness from an eight fringe shift | Block 2 | Full file only |
| Q5(b) | Step and graded index multimode profiles and modes | Block 4 | Full file only |
| Q5(c) | Grating spacing at 656 nm and unknown wavelength at 15.7ΒΊ | Block 3 | Full file only |
Programmes that include BPHCT 137 Waves and Optics
BPHCT 137 Waves and Optics is studied in two IGNOU science programmes, BSCG and BSCM.
In the IGNOU Bachelor of Science (General) programme it is a core course for students who choose Physics, taken alongside the other physics theory and lab courses of the scheme.
In the Bachelor of Science (Multidisciplinary) BSCM programme, offered under the four year undergraduate structure, the same BPHCT 137 paper is set, which is why the June 2026 paper prints both codes on its cover.
Its companion lab, BPHCL 138 Waves and Optics Laboratory, carries 2 credits and is examined separately, so lab work is not part of this solved paper.
How to get the full BPHCT 137 Solved Question Paper on WhatsApp
Send BPHCT 137 June 2026 on WhatsApp 9899436384 and we send the complete solved PDF with all 15 answers.
The process takes a few minutes. Message us with the course code and session, we confirm the price, and the PDF reaches you on the same chat once you confirm. The 13 parts locked on this page are all answered inside.
If you are also preparing for the December 2026 exam, mention it in the same message. We can tell you which Waves and Optics topics from the repeat table above deserve extra time.
BPHCT 137 Waves and Optics FAQs
Quick answers to what BSCG and BSCM students ask before ordering the BPHCT 137 file.
What is in the BPHCT 137 Solved Question Paper June 2026 file?
The full file solves all 15 parts of the June 2026 BPHCT 137 Waves and Optics paper. Numericals show formula, substitution and the final value in SI units. Derivations run line by line, and the diagrams the paper asks for, such as the Michelson interferometer and fibre index profiles, are drawn and labelled. Two of these answers are shown on this page as samples.
How do I get the full BPHCT 137 Waves and Optics solved file on WhatsApp?
Send a message to WhatsApp 9899436384 with the code BPHCT 137 and the session June 2026. Our team replies with the price and sends the complete solved PDF once you confirm. The file has answers for all 15 parts of the paper, which includes the 13 parts that are listed on this page as question text only.
Which BPHCT 137 questions are solved on this page?
Two BPHCT 137 answers are shown here in full. Q1(a) is the 65 tuning forks beats numerical, which works out the first fork at 256 Hz. Q2(c) is the derivation of resultant intensity for two superposed waves with constant phase difference. Every other part of the June 2026 paper appears on this page as question text only.
How is the BPHCT 137 June 2026 question paper structured?
The June 2026 BPHCT 137 paper carries 50 marks over 2 hours. It has five compulsory questions, each with three parts of 5 marks, and you answer any two parts of each question, so 10 parts in total. Calculators are allowed. This differs from the December 2025 paper, where Question 1 had eight short 2 mark parts.
Which BPHCT 137 Waves and Optics topics repeat most often?
In the six official BPHCT 137 papers we checked, the Michelson interferometer, standing waves on a string, polarisation, thin film and wedge fringes, optical fibres and lasers appeared in every session. Fresnel zones and zone plates, grating maxima and superposition intensity appeared in five of the six. These topics deserve the most revision time before the exam.
Are the BPHCT 137 answers suitable for Hindi medium students?
The BPHCT 137 solved file is written in simple English, which matches the English version of the paper printed in the same booklet. Formulae, numerical working and diagrams are language neutral, so Hindi medium students can follow them easily. If you need answers in Hindi, ask on WhatsApp 9899436384 before ordering so we can tell you what is available.
Does the BPHCT 137 solved paper include practical or lab work?
No. BPHCT 137 Waves and Optics is a 4 credit theory course, and its lab work sits in BPHCL 138 Waves and Optics Laboratory, a separate 2 credit course. The solved paper covers the theory term-end exam only. It does help with the lab viva, though, because Newton's rings, the grating and the Michelson interferometer appear in both places.
Who writes and checks the BPHCT 137 Waves and Optics answers?
BPHCT 137 answers are written by our physics subject experts after studying previous official Waves and Optics papers and the IGNOU block material. Every numerical is recalculated by a second person, and Sheetal Kirola reviews the final file for accuracy and exam fit before it is sent to students. Prateek Talwar is the author of record for the series.