In an experiment to measure the wavelength of monochromatic light, a diffraction pattern was produced using a diffraction grating with 500 lines per mm - Leaving Cert Physics - Question 3 - 2008

The first order images were identified by focusing the spectrometer on the bright fringe that appears on either side of the zero order image. This bright fringe is the nearest maxima to the zero order image, indicating the first order diffraction pattern.

To measure the angle between the first order images:

1. Set the crosshair of the spectrometer on the first order image on one side.
2. Read the angle indicated on the scale.
3. Focus on the corresponding first order image on the opposite side and take its reading.
4. Subtract the two angle measurements to find the angle between the first order images.

To calculate the wavelength of the monochromatic light, we can utilize the diffraction grating formula:

$n\,d = \sin(\theta) \; \rightarrow \; \lambda = \frac{d \cdot \sin(\theta)}{n}$

Where:

• $n$ = order of maxima (1 for first order),
• $d$ = distance between grating lines,
• $heta$ = angle measurement.

Given:

• Number of lines = 500 lines/mm, hence: $d = \frac{1}{500} \, \text{mm} = \frac{1}{500000} \, \text{m} = 2 \times 10^{-6} \, \text{m}$
• Angle between first order images = 34.2° Using one side of the angle:

$\lambda = \frac{2 \times 10^{-6} \, \text{m} \cdot \sin(34.2°)}{1} = 5.8808 \times 10^{-7} \, \text{m}$

Thus, the wavelength ( \lambda \approx 5.88 ; \text{nm} ).