Problem 2 IYPT 2027: 2. Disc spectrometer

Problem Description & Analysis

Data tracks on optical media (e.g. CDs / Blu-ray discs) behave as high-quality reflection-diffraction gratings. When illuminated, these discs can disperse light into its spectral components. Construct a spectrometer using a digital optical disc. Optimise the design to maximise the resolving power and minimise optical aberrations.

References & Further Reading

Textbooks

Hecht, E. (2017). Optics (5th ed.). Pearson. — Chapter 10: Diffraction and diffraction gratings; primary reference for grating equation, resolving power, and angular dispersion.
Born, M. & Wolf, E. (1999). Principles of Optics (7th ed.). Cambridge University Press. — §8.6: Diffraction gratings; rigorous mathematical treatment of the slit function and grating performance.
Hecht, E. & Zajac, A. (2003). Optics. Addison-Wesley. — Fraunhofer diffraction and gratings; excellent visual approach to the phenomenon.
Halliday, D., Resnick, R. & Walker, J. (2018). Fundamentals of Physics (11th ed.). Wiley. — Chapter 36: Diffraction; introductory-level coverage of grating equation and resolving power.
Pedrotti, F. L., Pedrotti, L. M. & Pedrotti, L. S. (2017). Introduction to Optics (3rd ed.). Cambridge University Press. — Chapter 13: Diffraction gratings and spectroscopic applications.

Research & Educational Articles

Wakabayashi, F., Hammaker, R. M. & Fateley, W. G. (1998). A new CD spectrometer for classroom demonstrations. Journal of Chemical Education, 75(1), 9–10. — Simple disc spectrometer construction and wavelength measurement of lasers.
Arnone, C. (1993). An inexpensive, CD-based spectrometer. The Physics Teacher, 31(7), 432–433. — Practical guide to building and calibrating a CD spectrometer.
Flügge, J. (1996). How to build a simple spectrograph using a compact disc. European Journal of Physics, 17(5), 299–304. — Quantitative analysis of CD performance as a reflection grating.
Greenslade, T. B. (2001). Diffraction grating from a compact disc. The Physics Teacher, 39(8), 471. — Practical tips for improving angular measurement accuracy.

Online Resources

Nave, C. R. HyperPhysics — Diffraction Grating. Georgia State University. — Visual explanation of grating equation and resolving power with interactive diagrams.
NIST Atomic Spectra Database. National Institute of Standards and Technology. — Reference spectral line database for spectrometer calibration.
Public Lab — DIY Spectrometry Kit (publiclab.org/wiki/spectrometry). — Open-source low-cost spectrometer project using a CD and webcam; includes community experimental data.
Spectroscopy Now — Educational Resources (spectroscopynow.com). — Educational articles on spectroscopy for students and researchers.

IYPT Resources

IYPT 2027 Official Problem Set — Problem 2: Disc Spectrometer. iypt.org — Official problem statement and grading guidelines.
IYPT Solutions Archive — Top-team solutions from previous years for related spectroscopy problems.

Educational Videos (YouTube)

Diffraction, Gratings, Spectral & Angular Resolution — Walter Lewin, MIT 8.03 (Lecture 21). Classic MIT lecture covering diffraction gratings, spectral and angular resolving power, with live demonstrations.
Diffraction, Resolution — MIT 8.03SC Physics III (Yen-Jie Lee). Lecture 22 from MIT Physics III; thorough coverage of Fraunhofer diffraction and its relationship to resolving power.
Diffraction grating | Light waves | Physics — Khan Academy. Introductory treatment of the grating equation with step-by-step numerical examples.
CDs and DVDs as Diffraction Gratings — F-J Physics. Demonstrates how CDs and DVDs act as reflection gratings and how to measure diffraction angles.
Lab: CD Spectrometer — MIT 6.S079 Nanomaker. Hands-on CD spectrometer lab from the MIT Nanomaker course.
Build your own CD Spectroscope — Exploratorium Science Snacks. Step-by-step guide to building a home spectrometer from a CD and cardboard, with physics explanation.

Open-Access Academic Papers

DeWeerd, A. J. (2016). CD, DVD, and Blu-Ray Disc Diffraction with a Laser Ray Box. The Physics Teacher, 54(5), 300–302. — Precise measurement of grating spacing for CD, DVD, and Blu-ray; comparison with manufacturer specifications. [Free PDF]
Wakabayashi, F. et al. (2002). Exploring the diffraction grating using a He-Ne laser and a CD-ROM. Journal of Chemical Education, 79(6), 703. — Using a He-Ne laser and CD to determine wavelength; calibration and error analysis. [Article page]
A DVD Spectroscope: A Simple, High-Resolution Classroom Spectroscope. ResearchGate. — Building a DVD-based spectrometer for higher resolution. [Open access]

University Lecture Notes (Open Access)

MIT OpenCourseWare — 2.71 Optics (Spring 2014): Lecture Notes. Complete MIT optics course notes covering Fraunhofer diffraction, gratings, and resolving power.
MIT OpenCourseWare — Physics III Ch.13: Interference and Diffraction (PDF). Full mathematical derivation of grating diffraction from the 8.03SC textbook.
OpenStax University Physics — Section 4.4: Diffraction Gratings. Free textbook chapter with angular dispersion, resolving power, and worked examples.
Physics LibreTexts — 4.05: Diffraction Gratings. Interactive online version with search and bookmarking.
SMU Physics — Diffraction and Compact Discs (PDF). SMU lab guide for measuring CD grating spacing with a laser; includes data table and error analysis.

Related Images

Disc

Interactive Simulation (Python)

This simulation runs directly in your browser — no Python installation needed. Initial loading may take a few seconds.

Grating spacing d 1.6 μm

Diffraction order m 1

Incident angle θᵢ 0 deg

Beam width 20 mm

Press the button below to start.

(a) Diffraction angle vs wavelength — colored curve from grating equation d·sin(θ) = m·λ; black points are student measurements with LEDs or lasers.
(b) Visible spectrum on screen — each color appears at a different angle; white dashed lines mark the measured LED positions.
(c) Measurement residuals (θ_measured − θ_theory) — deviations within ±0.5° indicate good experimental accuracy.

Python Code Lab

Edit this starter code, enter your own experimental data, and run it directly in the browser — no Python installation required.

Python — Editable

# ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
#  Code Lab: Disc Spectrometer (IYPT 2027 — Problem 2)
#  Edit this code, enter your own data, and run in browser
# ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

import numpy as np
import matplotlib.pyplot as plt

# ─── 1. Your experimental data ───────────────────────────
# Wavelengths of LEDs or lasers you used (nm)
lam_nm_data = np.array([405, 532, 589, 635, 650])   # <-- replace with your values

# Measured first-order diffraction angles (degrees)
theta_meas  = np.array([14.6, 19.5, 21.7, 23.4, 24.0])  # <-- your measurements

# Experiment parameters
d   = 1.6e-6   # CD grating spacing ≈ 1.6 μm  (DVD ≈ 0.74 μm)
m   = 1        # diffraction order
N   = 12500    # active slits (beam width / d)

# ─── 2. Theoretical model ────────────────────────────────
# Grating equation (normal incidence): sin(θ) = m·λ/d
lam_theory = np.linspace(380e-9, 780e-9, 500)
sin_th = m * lam_theory / d
mask   = sin_th <= 1.0
theta_theory = np.degrees(np.arcsin(np.clip(sin_th[mask], -1, 1)))
lam_theory_vis = lam_theory[mask] * 1e9   # nm

# Theoretical prediction for data points
theta_pred = np.degrees(np.arcsin(np.clip(m * lam_nm_data * 1e-9 / d, -1, 1)))
residuals  = theta_meas - theta_pred

# Resolving power
R = m * N
delta_lam = 550 / R   # min. resolvable delta-lambda at 550 nm

# ─── 3. Plots ────────────────────────────────────────────
fig, axes = plt.subplots(1, 3, figsize=(13, 4.5))
fig.suptitle('Disc Spectrometer — Measured vs Theory', fontsize=12, fontweight='bold')

def wl_to_rgb(w_nm):
    w = float(w_nm)
    if   w < 440: r,g,b = -(w-440)/60,  0,           1
    elif w < 490: r,g,b = 0,           (w-440)/50,   1
    elif w < 510: r,g,b = 0,            1,          -(w-510)/20
    elif w < 580: r,g,b = (w-510)/70,   1,            0
    elif w < 645: r,g,b = 1,          -(w-645)/65,   0
    else:         r,g,b = 1,            0,            0
    return (max(0,min(1,r)), max(0,min(1,g)), max(0,min(1,b)))

# Plot a: theta vs lambda
ax = axes[0]
for i in range(len(lam_theory_vis)-1):
    ax.plot(lam_theory_vis[i:i+2], theta_theory[i:i+2],
            color=wl_to_rgb(lam_theory_vis[i]), lw=2.5)
ax.scatter(lam_nm_data, theta_meas, color='#333', s=80, zorder=5,
           edgecolors='white', lw=1, label='Measured')
for lam_i, th_i in zip(lam_nm_data, theta_meas):
    ax.annotate(f'{lam_i}nm', (lam_i, th_i), textcoords='offset points',
                xytext=(5, 4), fontsize=7, color='#333')
ax.set_xlabel('Wavelength lambda (nm)')
ax.set_ylabel('Diffraction angle theta (deg)')
ax.set_title('(a) Grating Equation: sin(theta)=m*lam/d')
ax.legend(fontsize=8.5)
ax.grid(True, alpha=0.3, ls='--')
ax.set_xlim(370, 790)

# Plot b: color spectrum
ax = axes[1]
ax.set_facecolor('#111')
for i in range(len(lam_theory_vis)-1):
    ax.axvspan(theta_theory[i], theta_theory[i+1],
               color=wl_to_rgb(lam_theory_vis[i]), alpha=0.95)
for lam_i, th_i in zip(lam_nm_data, theta_meas):
    ax.axvline(th_i, color='white', lw=1.5, ls='--', alpha=0.8)
    ax.text(th_i, 0.05, f'{lam_i}', transform=ax.get_xaxis_transform(),
            fontsize=7, color='white', ha='center')
ax.set_xlim(theta_theory.min(), theta_theory.max())
ax.set_xlabel('Diffraction angle (deg)')
ax.set_yticks([])
ax.set_title('(b) Spectrum — white dashes = your LEDs')

# Plot c: residuals
ax = axes[2]
colors_data = [wl_to_rgb(lam_i) for lam_i in lam_nm_data]
bars = ax.bar(lam_nm_data, residuals, width=18,
              color=colors_data, alpha=0.85, edgecolor='#333', lw=0.8)
ax.axhline(0, color='#333', lw=1.5, ls='--')
ax.axhline( 0.5, color='#aaa', lw=1, ls=':', alpha=0.7)
ax.axhline(-0.5, color='#aaa', lw=1, ls=':', alpha=0.7)
ax.text(lam_nm_data[-1]+8, 0.52, '+/-0.5 deg', fontsize=7.5, color='#888')
for bar, res in zip(bars, residuals):
    ax.text(bar.get_x()+bar.get_width()/2, res + (0.05 if res>=0 else -0.12),
            f'{res:+.2f}', ha='center', fontsize=8, fontweight='bold')
ax.set_xlabel('Wavelength (nm)')
ax.set_ylabel('Residual theta_meas - theta_theory (deg)')
ax.set_title('(c) Measurement Error (Residuals)')
ax.grid(True, axis='y', alpha=0.3, ls='--')
for sp in ['top','right']: ax.spines[sp].set_visible(False)


# ── Watermark ────────────────────────────────────────────────────────────────
for _wx in [0.18, 0.50, 0.82]:
    for _wy in [0.22, 0.52, 0.80]:
        fig.text(_wx, _wy, 'physicsme.ir',
                 fontsize=16, color='#b0b8cc', alpha=0.22,
                 ha='center', va='center', rotation=30,
                 transform=fig.transFigure, fontweight='bold', style='italic')
        fig.text(_wx, _wy - 0.055, 'man_e fizikee',
                 fontsize=10, color='#b0b8cc', alpha=0.22,
                 ha='center', va='center', rotation=30,
                 transform=fig.transFigure, fontweight='bold', style='italic')
fig.text(0.98, 0.012, '© physicsme.ir  ·  man_e fizikee',
         fontsize=8, color='#888', alpha=0.75,
         ha='right', va='bottom', transform=fig.transFigure)
plt.tight_layout()

# ─── 4. Numerical summary ─────────────────────────────────
print(f"Grating: d = {d*1e6:.2f} um  ({1e-3/d*1e6:.0f} lines/mm)")
print(f"Order: m = {m}")
print(f"Resolving power: R = m*N = {R}  ->  min delta_lam ~ {delta_lam:.2f} nm at 550nm")
print(f"RMS error: {np.sqrt(np.mean(residuals**2)):.3f} deg")
print(f"Max error: {np.max(np.abs(residuals)):.3f} deg at {lam_nm_data[np.argmax(np.abs(residuals))]} nm")

Ready to run

Output