Determining wavelength using a diffraction grating (PAG 4)
Determine the wavelength of monochromatic light using a diffraction grating; also investigate Young's double slit fringes.
Apparatus
- Laser or bright monochromatic source
- Diffraction grating (known lines per mm)
- Double slit card
- Screen, metre rule
- Protractor or spectrometer
Safety
- Never look into the laser beam directly.
- Display a laser warning sign and ensure the beam cannot reach anyone's eyes.
Method
- Diffraction grating: direct laser through grating onto screen. Measure distance D to screen and distances $y_n$ to each order n.
- Calculate $\tan\theta = y_n/D$; apply $d\sin\theta = n\lambda$ for each order.
- Young's slits: direct laser through double slit. Measure fringe spacing w and slit-screen distance D.
- Calculate $\lambda = aw/D$ where a is slit separation.
- Compare wavelengths obtained by both methods.
Key Variables
Independent
Order n (grating) or distance D (Young's)
Dependent
Angle theta (grating) or fringe spacing w (Young's)
Controlled
Same laser throughout; Grating/slit properties constant
Analysis and Results
- Grating: $d\sin\theta = n\lambda$. Plot $\sin\theta$ vs n: gradient $= \lambda/d$.
- Young's slits: $\lambda = aw/D$. Measure w across many fringes to reduce uncertainty.
- Both methods should yield consistent values of $\lambda$.
Common Errors
- Using $\theta = y/D$ (small angle approximation) for large angles (grating).
- Measuring fringe spacing across too few fringes in Young's slits.
- Confusing $d$ (slit spacing) with $N$ (lines per mm).
Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.
Q13 marks
A grating with 500 lines mm$^{-1}$ gives a second-order maximum at 38.5 degrees. Calculate the wavelength.
Q22 marks
Explain why using the second-order maximum rather than the first gives a more precise measurement of wavelength.