Determination of wavelength using a diffraction grating (CP6)
Determine the wavelength of monochromatic light using a diffraction grating.
Apparatus
- Laser or monochromatic light source with filter
- Diffraction grating (known line spacing d)
- Screen and ruler (or spectrometer with protractor)
- Metre rule
Safety
- Never look directly into the laser. Post a warning sign on the door.
- Ensure no specular reflections from the grating or screen surface can leave the lab.
Method
- Direct the laser through the diffraction grating onto a screen ~1.0 m away.
- Measure the distance D from grating to screen and the distances $y_n$ from the central maximum to each order n.
- Calculate $\tan\theta_n = y_n/D$, hence $\theta_n = \arctan(y_n/D)$.
- Apply $d\sin\theta_n = n\lambda$ to find $\lambda$ for each order.
- Average the values of $\lambda$ obtained from orders n = 1 and n = 2 (and $n = -1$, $-2$ if visible).
Key Variables
Independent
Order number n
Dependent
Diffraction angle theta
Controlled
Line spacing d (same grating); Wavelength (same laser)
Analysis and Results
- $d\sin\theta = n\lambda$. Plot $\sin\theta$ vs n: straight line through origin, gradient $= \lambda/d$.
- Check that $\sin\theta < 1$ for all measured orders (beyond this, no diffraction maximum exists).
- A spectrometer gives more precise angle measurements than a ruler and screen.
Common Errors
- Measuring the angle from the wrong side of the central maximum.
- Using $\theta = y/D$ instead of $\tan\theta = y/D$ (significant error for large angles).
- Confusing d (slit spacing in metres) with N (lines per mm or per metre).
Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.
Q13 marks
A laser passes through a grating with 600 lines mm$^{-1}$. The first-order maximum appears at 21.1 degrees. Calculate the wavelength.
Q22 marks
Explain why a grating with 600 lines mm$^{-1}$ produces sharper maxima than one with 100 lines mm$^{-1}$.